Research:

Publications (since 2000) | Preprints | Talks

Publications:

Almost fine gradings on algebras and classification of gradings up to isomorphism (with Mikhail Kochetov); Doc. Math. 30 (2025), 887-908. (Preprint arXiv:2308.07230.)
From the Albert algebra to Kac's ten-dimensional Jordan superalgebra via tensor categories in characteristic 5 (with Pavel Etingof and Arun S. Kannan); J. Algebra 666 (2025), 387-414. (Preprint arXiv:2404.01719.)
From octonions to composition superalgebras via tensor categories (with Alberto Daza-García and Umut Sayin); Rev. Mat. Iberoam. 40 (2024), no. 1, 129-152. (Preprint arXiv:2205.06559.)
Short (SL₂xSL₂)-structures on Lie algebras (with Patricia D. Beites, Alejandra S. Córdova-Martínez and Isabel Cunha); Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118 (2024), no. 2, paper no. 45 (21 pages, doi 10.1007/s13398-023-01541-4). (Preprint arXiv:2303.17993.)
Okubo algebras with isotropic norm; in Non-Associative Algebras and Related Topics. NAART 2020, 287-301. Edited by H. Albuquerque, J. Brox, C. Martínez, and P. Saraiva. Springer Proceedings in Mathematics & Statistics, vol 427, Springer, Cham, 2023. (Preprint arXiv:2210.03456.)
Local derivations and automorphisms of Cayley algebras (with Shavkat Ayupov and Karimbergen Kudaybergenov); J. Pure Appl. Algebra (2023), 107277 (16 pages, doi 10.1016/j.jpaa.2022.107277). (Preprints arXiv:2105.08423 and arXiv:2205.06559.)
Real simple symplectic triple systems (with Cristina Draper); Anal. Math. Phys. 12 (2022), paper no. 69, 46 pp. (Preprint arXiv:2107.05882.)
Non-group gradings on simple Lie algebras; Linear Algebra Appl. 640 (2022), 149-161. (Preprint arXiv:2107.13791.)
Gradings on associative algebras with involution and real forms of classical simple Lie algebras (with Mikhail Kochetov and Adrián Rodrigo-Escudero); J. Algebra 590 (2022), 61-138. (Preprint arXiv:2105.13666.)
Graded-division algebras and Galois extensions (with M. Kochetov); J. Pure Appl. Algebra 221 (2021), 106773. (Preprint arXiv:2008.06212.)
Evolution algebras, automorphisms, and graphs (with A. Labra); Linear Multilinear Algebra 69 (2021), no. 2, 331-342. (Preprint arXiv:1902.02191.)
Graded-division algebras over arbitrary fields (with Y. Bahturin and M. Kochetov); J. Algebra Appl. 20 (2021), no. 1, 2140009, 28 pages. (Preprint arXiv:1912.11911.)
Cross products, automorphisms, and gradings (with A. Daza-García and L. Tang); Linear Algebra Appl. 610 (2021), 227-256. (Preprint arXiv:2006.10324.)
Composition algebras; in Algebra and Applications I: Non-associative Algebras and Categories, Chapter 2, pp. 27-57, edited by Abdenacer Makhlouf, Sciences-Mathematics, ISTE-Wiley, London 2021. (Preprint arXiv:1810.09979.)
Codes, S-structures, and exceptional Lie algebras (with I. Cunha); Glasgow Math. J. 62 (2020), S14-S27. (Preprint arXiv:1812.08439.)
Reductive homogeneous spaces and nonassociative algebras; Commun. Math. 28 (2020), no. 2, 199-229. (Preprint arXiv:1503.03227.)
Graded-simple algebras and cocycle twisted loop algebras; Proc. Amer. Math. Soc. 147 (2019), no. 7, 2821-2833. (Prepint arXiv:1807.01041.)
On Kac's Jordan superalgebra (with A.S. Córdova-Martínez and Abbas Darehgazani); Linear Multilinear Algebra 67 (2019), no. 3, 490-498. (Preprint arXiv:1701.06798.)
Gradings on semisimple algebras (with Alejandra Sarina Córdova Martínez); Linear Algebra Appl. 559 (2018), 145-171. (Preprint arXiv:1803.09959.)
Gradings on the simple real Lie algebras of types G₂ and D₄ (with Mikhail Kochetov); J. Algebra 512 (2018), 382-426. (Preprint arXiv:1803.10949.)
Order 3 elements in G₂ and idempotents in symmetric composition algebras; Canadian J. Math. 70 (2018), no. 5, 1038-1075. (Preprint arXiv:1705.01293.)
Clifford algebras as twisted group algebras and the Arf invariant (with Adrián Rodrigo-Escudero); Adv. Appl. Clifford Algebras (2018), 28:41. (Preprint arXiv:1801.07002.)
Cross products, invariants, and centralizers (with G. Benkart); J. Algebra 500 (2018), 69-102. (Preprint arXiv:1606.07588.)
Gradings on modules over Lie algebras of E types (with C. Draper and M. Kochetov); Algebras and Representation Theory 20 (2017), no. 5, 1085-1107. (Preprint arXiv:1609.02510.)
Maximal finite abelian subgroups of E₈ (with C. Draper); Proc. Royal Soc. Edinburgh 147A (2017), 993-1008. (Preprint arXiv:1312.4326.)
Graded simple modules and loop modules (with M. Kochetov); in “Groups, Rings, Group Rings and Hopf Algebras”, dedicated to Don Passman. Contemporary Mathematics, volume 688 (2017), pp. 53-85. (Preprint arXiv:1601.03008.)
Gradings on algebras over algebraically closed fields; in Non-Associative and Non-Commutative Algebra and Operator Theory. NANCAOT, Dakar, Senegal, May 23-25, 2014: Workshop in Honor of Professor Amin Kaidi, Gueye, Cheikh Thiecoumbe, Molina, Mercedes Siles (Eds.), pp. 113-121, Springer 2016. (Preprint arXiv:1407.0480.)
An overview of fine gradings on simple Lie algebras (with C. Draper); Note Mat. 36 (2016), 15-34. (Preprint arXiv:1603.09482.)
On nilpotent evolution algebras (with A. Labra); Linear Algebra Appl. 505 (2016), 11-31. (Preprint arXiv:1602.01590.)
Some special features of Cayley algebras, and G₂, in low characteristics (with A. Castillo-Ramírez); J. Pure Appl. Algebra. 220 (2016), no. 3, 1188-1205. (Preprint arXiv:1503.05529.)
Okubo algebras: automorphisms, derivations and idempotents; Contemporary Mathematics, vol. 652, Amer. Math. Soc. Providence, RI, 2015, pp. 61-73.
Proceedings of the Bicocca-Workshop on Lie Algebras 2013, in honor of Professor Helmut Strade on the occasion of his 70th birthday, Milano, May 22nd-24th, 2013; Marina Avitabile, Joerg Feldvoss, and Thomas Weigel, eds.
(Preprint arXiv:1310.5455.)
Gradings on the Lie algebra D₄ revisited (with M. Kochetov); J. Algebra 441 (2015), 441-474. (Preprint arXiv:1412.5076.)
Graded modules over classical simple Lie algebras with a grading (with M. Kochetov); Israel J. Math. 207 (2015), no. 1, 229-280. (Preprint arXiv:1308.6089.)
Evolution algebras and graphs (with A. Labra); J. Algebra Appl. 14 (2015), no. 7, 1550103 (10 pages). (Preprint arXiv:1312.4685.)
Fine gradings and gradings by root systems on simple Lie algebras; Revista Matemática Iberoamericana 31 (2015), no. 1, 245-266. (Preprint arXiv:1303.0651.)
Fine gradings on the simple Lie algebras of type E (with C. Draper); Note Mat. 34 (2014), no. 1, 53-88. (Preprint arXiv:1403.0514.)
Left unital Kantor triple systems and structurable algebras (with N. Kamiya and S. Okubo); Linear and Multilinear Algebra 62 (2014), no. 10, 1293-1313. (Preprint arXiv:1205.2489.)
Classification of quadratic Lie algebras of low dimension (with S. Benayadi); J. Math. Phys. 55 (2014), 081703. (Preprint arXiv:1404.5174.)
A Z₄³-grading on a 56-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E (with D. Aranda-Orna and M. Kochetov); Comment. Math. Univ. Carolin. 55 (2014), no. 3, 285-313. (Preprint arXiv:1312.1067.)
Gradings on simple Lie algebras (with M. Kochetov), Mathematical Surveys and Monographs 189, American Mathematical Society, 2013.
Algebraic Groups of Type D₄, Triality, and Composition Algebras (with V. Chernousov, M. Knus and J.-P. Tignol); Documenta Math. 18 (2013), 413-468.
On some Jordan baric algebras (with A. Labra); J. Algebra Appl. 12 (2013), no. 5, 1250215 (12 pages). (Preprint arXiv:1205.2993.)
Weyl groups of fine gradings on simple Lie algebras of types A, B, C and D (with M. Kochetov), Serdica Math. J. 38 (2012), 7-36. (Preprint arXiv:1109.3540.)
Lie algebras with prescribed sl₃ decomposition (with G. Benkart), Proc. Amer. Math. Soc. 140 (2012), no. 8, 2627--2638. (Preprint arXiv:1101.0489.)
Weyl groups of fine gradings on matrix algebras, octonions and the Albert algebra (with M. Kochetov), J. Algebra 366 (2012), no. 1, 165-186. (Preprint arXiv:1009.1462.)
Gradings on the exceptional Lie algebras F₄ and G₂ revisited (with M. Kochetov), Rev. Mat. Iberoamericana 28 (2012), no. 3, 775-815. (Preprint arXiv:1009.1218.)
A class of Locally Nilpotent Commutative Algebras (with A. Behn and A. Labra), Internat. J. Algebra Comput. 21 (2011), no. 5, 763-774. (Preprint arXiv:0907.3569.)
Fine gradings on exceptional simple Lie superalgebras (with C. Draper and C. Martín-González), International Journal of Mathematics 22 (2011), no. 12, 1823-1855. (Preprint arXiv:1101.5470.)
Special Freudenthal-Kantor triple systems and Lie algebras with dicyclic symmetry (with S. Okubo), Proc. Royal Soc. Edinburgh 141A (2011), no. 6, 1225-1262. (Preprint arXiv:1004.1125.)
Tits construction of the exceptional simple Lie algebras, Pure and Applied Mathematics Quarterly 7 (2011), no. 3 (Special Issue: In honor of Jacques Tits), 559-586. (Preprint arXiv:0907.3789.)
Derivations of the Cheng-Kac Jordan superalgebras (with E. Barreiro and C. Martínez), J. Algebra 338 (2011), no. 1, 144-156. (Preprint arXiv:1101.0485.)
Irreducible Lie-Yamaguti algebras of generic type (with P. Benito and F. Martín-Herce), J. Pure Applied Algebra 215 (2011), 108-130. (Preprint arXiv:0907.3622.)
Fine gradings on simple classical Lie algebras, J. Algebra 324 (2010), no. 12, 3532-3571. (Preprint arXiv:0906.0655.)
Gradings on symmetric composition algebras, J. Algebra 322 (2009), no. 10, 3542-3579. (Preprint arXiv:0809.1922.)
Jordan gradings on the exceptional simple Lie algebras, Proc. Amer. Math. Soc. 137 (2009), no. 12, 4007-4017. (Preprint arXiv:0810.2737.)
More non semigroup Lie gradings, Linear Algebra Appl. 431 (2009), no. 9, 1603-1606. (Preprint arXiv:0809.4547.)
The Supermagic Square in characteristic 3 and Jordan superalgebras (with Isabel Cunha), Algebras, Representations and Applications. Proceedings of a Conference in Honour of Ivan Shestakov's 60th Birthday (Maresias, Brazil 2007). Contemporary Mathematics 483 (2009), 91-106. (Preprint arXiv:0802.3271)
Lie algebras with S₃ or S₄-action and generalized Malcev algebras (with Susumu Okubo), Proc. Royal Soc. Edinburgh 139A (2009), 321-357. (Preprint arXiv:0801.2481)
Irreducible Lie-Yamaguti algebras (with Pilar Benito and Fabián Martín-Herce), J. Pure Applied Algebra 213 (2009), 795-808. (Preprint arXiv:0810.0440)
Models of some simple modular Lie superalgebras, Pacific J. Math. 240 (2009), no. 1, 49-83. (Preprint arXiv:0805.1304)
The Tits construction and some simple Lie superalgebras in characteristic 3, J. Lie Theory 18 (2008), no. 3, 601-615. (Preprint arXiv:math.RA/0703784. A review of this paper appears in the Excerpts from Zentralblatt MATH. Special Issue ICM 2010, Hyderabad)
Maximal subalgebras of Jordan superalgebras (with Jesús Laliena and Sara Sacristán), J. Pure Appl. Algebra 212 (2008), no. 11, 2461-2478. (Preprint arXiv:math.RA/0606017)
S₄-symmetry on the Tits construction of exceptional Lie algebras and superalgebras (with Susumu Okubo), Publ. Mat. 52 (2008), no. 2, 315-346. (Preprint arXiv:math.RA/0611303)
Wedderburn quasialgebras (with Helena Albuquerque and José María Pérez-Izquierdo), Portugal Math. (N.S.) 65 (2008), no. 2, 275-283.
On the classification of commutative right nilalgebras of nilindex 5 and dimension 4 (with Alicia Labra), Commun. Algebra 36 (2008), 1704-1716. (Preprint of the 'Seminario García Galdeano'.)
The existence of superinvolutions (with Oliver Villa), J. Algebra 319 (2008), 4338-4359. (Preprint arXiv:0704.3127)
Symplectic and orthogonal triple systems, and a Freudenthal Magic Supersquare, Proceedings of the "XVI Coloquio Latinoamericano de álgebra" (Colonia de Sacramento, Uruguay, 2005), Biblioteca de la Revista Matemática Iberoamericana (2007), 253-270. (Preprint of the 'Seminario García Galdeano'.)
The S₄-action on the Tetrahedron Algebra, Proc. Royal Soc. Edinburgh 137A (2007), 1227-1248. (Preprint arXiv:math.RA/0604218)
Some new simple modular Lie superalgebras, Pacific J. Math. 231 (2007), no. 2, 337-359. (Preprint arXiv:math.RA/0512654)
An extended Freudenthal Magic Square in characteristic 3 (with Isabel Cunha), J. Algebra 317 (2007), 471-509. (Preprint arXiv:math.RA/0605379)
The Kac Jordan superalgebra: automorphisms and maximal subalgebras (with Jesús Laliena and Sara Sacristán), Proc. Amer. Math. Soc.135 (2007), no. 12, 3805-3813. (Preprint arXiv:math.RA/0509040)
The extended Freudenhtal Magic Square and Jordan algebras (with Isabel Cunha), manuscripta math. 123 (2007), no. 3, 325-351. (Preprint arXiv:math.RA/0608191)
The magic square and symmetric compositions II; Rev. Mat. Iberoamericana 23 (2007), 57-84.(Preprint arxiv:math.RT/0507282)
On the classification of commutative right-nilalgebras of dimension at most four (with Alicia Labra); Commun. Algebra 35 (2007), no. 2, 577-588. (Preprint of the 'Seminario García Galdeano'.)
Lie algebras with S₄-action and structurable algebras (with Susumu Okubo), J. Algebra 307 (2007), 864-890. (Preprint arXiv:math.RA/0508558)
Freudenthal's magic supersquare in characteristic 3 (with Isabel Cunha); From Lie Algebras to Quantum Groups (H. Albuquerque, S. Lopes and J. Teles eds.), Centro Internacional de Matemática, Coimbra (Portugal) 2006, pp. 17-25. (Preprint of the 'Seminario García Galdeano'.)
A Lie grading which is not a semigroup grading; Linear Algebra and Appl. 418 (2006), 312-314. (Preprint arXiv:math.RA/0512618)
A new look at Freudenthal's magic square, in Non Associative Algebra and Its Applications, (L. Sabinin, L. Sbitneva and I.P. Shestakov, eds.); Lecture Notes in Pure and Applied Mathematics, vol. 246, pp. 149-165. Chapman and Hall, Boca Raton 2006. (Preprint of the 'Seminario García Galdeano'.)
New simple Lie superalgebras in characteristic 3; J. Algebra 296 (2006), 196-233. (Preprint arXiv:math.RA/0412395)
(-1,-1)-balanced Freudenthal Kantor triple systems and noncommutative Jordan algebras (with Noriaki Kamiya and Susumu Okubo); J. Algebra 294 (2005), 19-40. (Preprint arXiv:math.RA/0404550)
Lie-Yamaguti algebras related to g₂ (with Pilar Benito and Cristina Draper); J. Pure Appl. Algebra 202 (2005), 22-54.
A Note on the Linkage of Hurwitz Algebras (with Oliver Villa); manuscripta math. 117 (2005), 15-110. (Preprint of the 'Seminario García Galdeano'.)
Symmetric Composition Algebras and Freudenthal's Magic Square; Resenhas IME-USP 6 (2004), no. 2/3, 165-176.
A(n,n)-graded Lie superalgebras (with Georgia Benkart and Consuelo Martínez); J. Reine Angew. Math. 573 (2004), 139-156. (Preprint arXiv:math.RT/0309395)
The magic square and symmetric compositions; Revista Mat. Iberoamericana 20 (2004), no. 2, 475-491. (Preprint Jordan Theory Preprint Archives 130, June 2002)
A modified Brauer algebra as centralizer algebra of the unitary group; Trans. Amer. Math. Soc. 356 (2004), no. 10, 3963-3983. (Preprint arXiv:math.RT/0305429)
Maximal subalgebras of associative superalgebras (with J. Laliena and S. Sacristán); J. Algebra 275 (2004), 40-58.
Composition algebras satisfying the flexible law (with Hyo Chul Myung); Commun. Algebra 32(5) (2004), 1997-2013.
Quaternions, octonions and the forms of the exceptional simple classical Lie superalgebras; Comment. Math. Helv. 79 (2004), no. 1, 208-228.
Nonassociative systems and irreducible homogeneous spaces (with Pilar Benito and Fabián Martín Herce); in "Recent Advances In Geometry and Topology". The 6th International Workshop on Differential Geometry and Topology and The 3rd German-Romanian Seminar on Geometry. Cluj-Napoca, September 1-6 2003, pp. 65-76. (Preprint of the 'Seminario García Galdeano'.)
Lie superalgebras graded by the root system A(m,n) (with Georgia Benkart); J. Lie Theory 13 (2003), 387-400. (Preprint arXiv:math.RA/0202284)
Lie superalgebras graded by the root system B(m,n) (with Georgia Benkart); Selecta math., New ser. 9 (2003), 313-360.
Simple (-1,-1) balanced Freudenthal Kantor triple systems (with Noriaki Kamiya and Susumu Okubo); Glasgow Math. J. 45 (2003), 353-372.
Models of the octonions and G₂ (with M.P. Benito and C. Draper), Linear Algebra Appl. 371 (2003), 333-359.
The Tits construction and the exceptional simple classical Lie superalgebras (with Georgia Benkart), Quartely J. Math. 54 (2003), 123-137.
Lie superalgebras graded by the root systems C(n), D(m,n), D(2,1;a), F(4), and G(3) (with Georgia Benkart), Canadian Math. Bull. 45 (4) (2002), 509-524.
Composition superalgebras (with Susumu Okubo), Commun. Algebra 30 (2002), no. 11, 5447-5471.
A new construction of the Kac Jordan superalgebra (with Georgia Benkart), Proc. Amer. Math. Soc. 130 (2002), no.11, 3209-3217.
Composition of quadratic forms and the Hurwitz-Radon function in characteristic 2, Linear Algebra Appl. 348 (2002), 87-103.
Z₂-quasialgebras (with H. Albuquerque and J.M. Pérez-Izquierdo), Commun. Algebra 30(5) (2002), 2161-2174.
On the Cartan Jacobson theorem (with P. Alberca Bjerregaard, C. Martín González and F.J. Navarro Márquez), J. Algebra 250 (2002), 397-407.
Local triality and some related algebras (with S. Okubo), J. Algebra 244 (2001), 828-844.
Alternative Quasialgebras (with H. Albuquerque and J.M.Pérez-Izquierdo), Bull. Australian Math. Soc. 63 (2001), 257-268.
Invariant projectively flat affine connections on Lie groups, Hokkaido Math. J. 30 (2001), 231-239.
A note on triality and symmetric compositions, Abh. Math. Sem. Univ. Hamburg 70 (2000), 125-135. (http://dx.doi.org/10.1007/BF02940909)
Power associative composition algebras (with J.A. Cuenca and J.M. Pérez-Izquierdo), manuscripta math. 103 (2000), 75-90.
On algebras satisfying x²x²=N(x)x (with S. Okubo), Math. Z. 235 (2000), no. 2, 275-314.
Triality and automorphisms and derivations of composition algebras, Linear Algebra Appl. 314 (2000), 49-74.
Octonions and affine connections on spheres (with H.C. Myung), Nonassociative Algebra and Its Applications (R. Costa, H. Guzzo Jr., A. Grichkov and L.A. Peresi, eds.), Lecture notes in pure and applied mathematics 211, 43-54. Marcel-Dekker, Nueva York 2000.
Invariant connections on symmetric spaces (with C. Draper and M.P. Benito), Nonassociative Algebra and Its Applications (R. Costa, H. Guzzo Jr., A. Grichkov and L.A. Peresi, eds.), Lecture notes in pure and applied mathematics 211, 21-33. Marcel-Dekker, Nueva York 2000.
The Reductive Pair (B₄,B₃) and Affine Connections on S¹⁵ (with H.C. Myung), J. Algebra 227 (2000), 504-531.
Pseudo-composition superalgebras (with S. Okubo), J. Algebra 227 (2000), 1-25.

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Preprints:

Automorphism group schemes and Weyl groups of gradings ; arXiv:2507.12321.
Special pure gradings on simple Lie algebras of types E₆, E₇, E₈ (with Cristina Draper and Mikhail Kochetov); arXiv:2507.03762.
J-ternary algebras, structurable algebras, and Lie superalgebras (with Isabel Cunha); arXiv:2506.18486.

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Talks:

From the Albert algebra to Kac's ten-dimensional Jordan superalgebra. Algebras and Forms in Geometry and Beyond (In honour of Saïd Benayadi for his 60th anniversary), Université de Haute Alsace, Mulhouse (France), September 11-12, 2025.

From algebras to superalgebras via tensor categories

Hopf Algebras and Related Topics

Giros y cuaterniones

A few exceptional algebras. Joint Meeting of the NZMS, AustMS and AMS, Special Session 50 Years of Communications in Algebra; Auckland, New Zealand, December 9-13, 2024.
Gradings on simple Lie algebras: old and new. Escola de Álgebra XXVII (XXVII Brazilian Algebra Meeting), Institute of Mathematics and Statistics, University of São Paulo (IME-USP), Brazil, July 15-19, 2024.
Gradings by root systems and S-structures on Lie algebras. Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart (SLMath, May 1-3, 2024).
The extended Freudenthal magic square via tensor categories. Symmetric Tensor Categories and Representation Theory (IPAM, January 8-12, 2024).
Gradings and S-structures on Lie algebras. VI International Workshop on Non-Associative Algebras (Madrid, Spain, June 19-23, 2023) and Groups, Rings, Lie and Hopf Algebras. V (Memorial University of Newfoundland, Harlow campus, UK, August 21-25, 2023).
Tensor categories, algebras, and superalgebras. European Non-Associative Algebra Seminar (January 9, 2023); Virtual conference Representations of Lie Superalgebras and Related Topics, School of Mathematics, IPM-Isfahan (Iran; August 31 - September 1, 2023); Seminar Lie and Jordan Algebras and their Representations, Universidade de Sao Paulo (Brasil; August 18, 2022); Non-Associative Algebras and Related Topics II (NAART II, July 18-22, 2022); and Universidad de Málaga (June 21, 2022).
(Here you may get the slides of the talk.)
Quaternions and octonions. Seminar of the School of Mathematical Sciences of Harbin Normal University (China, December 13, 2022).
Gradings on simple Lie algebras. Online seminar Quadratic forms, Linear algebraic groups and Beyond, January 26, 2022; and Tianyuan Mathematical Center in Southeast China, February 28, 2020.
(Here you may get the slides of the talk.)
Non-group gradings on simple Lie algebras. International Conference Trends in Combinatorial Ring Theory (Dedicated to the 70th anniversary of Vesselin Drensky). Sofia (Bulgaria, September 20-24, 2021), and RSME2022 (Congreso bienal de la Real Sociedad Matemática Española, Ciudad Real, Spain, January 17-22, 2022)
Composition algebras. Online mini-course (5 lectures) at the CIMPA School Non-associative algebras and their Applications August 30 to September 11, 2021. University of Antananarivo (Madagascar).
(Here you may get the slides of the course.)
Graded-division algebras and Galois extensions. International Conference on ring Theory, dedicated to the 100th anniversay of A.I. Shirshov (1921-1981). Novosibirsk (Russia, August 16-21).
(Here you may get the slides of the talk.)
Gradings and affine group schemes. Online mini-course (4 lectures) at the University of Isfahan (Iran, June-July 2021).
Graded-simple algebras and twisted loop algebras. Online seminar Lie and Jordan Algebras and their Representations. Universidade de Sao Paulo (Brasil; October 8, 2020).
(Here you may get the slides of the talk.)
Codes, S-structures, and exceptional Lie algebras, III International Workshop on Non-Associative Algebras. Universidad de Málaga (Spain; February 3-7, 2020).
Triality, Workshop on Differential Geometry and Nonassociative Algebras. CIRM Luminy (France; November 12-15, 2019).
Clifford algebras as twisted group algebras and the Arf invariant, Dia de Álgebra, dedicado a Helena Albuquerque, por ocasião do seu aniversário. Universidade de Coimbra (Portugal; September 27, 2019).
Graded-simple algebras and loop algebras, International Workshop on Non-Associative Algebras in Porto (Portugal; April 29 - May 3, 2019), and International Workshop on Nonassociative Algebras and Geometry, Bonne Bay Marine Station, Memorial University of Newfoundland (Canada, August 12-16, 2019).
Gradings on semisimple algebras, Workshop on Non-Associative Algebras and Applications, Lancaster University (UK; July 9-13, 2018).
Quaternions and Octonions, International Workshop Combinatorics of Group Actions and its Applications, Memorial University of Newfoundland (Canada; August 28 to September 1, 2017), and Fourth International Colloquium on Representations of Algebras and its Applications; Alexander Zavadskij (National University of Colombia; November 4-6, 2020).
Order 3 elements in G₂ and idempotents in symmetric compostion algebras, "Lie Theory, Cohomology, and Geometry in Wildrose Country", a workshop in honour of Vladimir Chernousov and Arturo Pianzola; University of Alberta (Edmonton, Canada; August 21 to 25, 2017); and II Joint Meeting Spain-Brazil in Mathematics (Cádiz, Spain; December 11 to 15, 2018).
Cross products, invariants, and centralizers, Universidad de Málaga, (Spain; July 17, 2017), and the International Workshop "Combinatorics of Group Actions and its Applications", Memorial University of Newfoundland (Canada; August 28 to September 1, 2017).
Triality, Congreso Bienal de la Real Sociedad Matemática Española, Universidad de Zaragoza, (Spain; January 30 to February 3, 2017).
Graded simple algebras and modules, Workshop on Non-Associative Algebras and Other Structures, Universidad de Málaga, (Spain; December 14 and 15, 2016).
Okubo algebras, Conference in honor of Ernst Dieterich and Karl-Heinz Fieseler, Uppsala University, (Sweden; September 15, 2016).
Graded modules over simple Lie algebras, International Conference "Groups and Rings - Theory and Applications" (GRiTA2016), Sofia (Bulgaria; July 11-15, 2016).
Gradings on simple Lie algebras, Jilin University, November 13, 2020; Algebra Seminar, Chalmers University of Technology and the University of Gothenburg, March 10, 2016; and “Workshop on Graded Algebra, Geometry and Related Topics” (Honoring the 60th birthday of O. Adolfo Sánchez-Valenzuela), Mérida (México, November 15-18, 2016).
Here is a video of this last talk.
Octonions in low characteristics, First joint meeting Brazil-Spain in Mathematics, Fortaleza (December 7-10, 2015); XXI Coloquio Latinoamericano de Álgebra, Buenos Aires (July 24-29, 2016); and “Les Deuxièmes Journées de Géometrie, et Algèbre Non Associative”, Meknès (October 6-8, 2016).
Octonions, Combinatorics Seminar, University of Wisconsin, November 9, 2015; Colloquium Talk, Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, March 11, 2016; and Colloquium Talk, Department of Mathematics, Uppsala University, September 16, 2016.
Gradings on simple Lie algebras, (a three-hours minicourse). Advances in Group Theory and Applications AGTA2015, Porto Cesareo (June 16-19, 2015).
Triality, composition algebras, and gradings on D₄. Minisymposium “Algebras and Algebraic Groups”, Uppsala (May 22, 2015); and “Lie and Jordan Algebras VI. Dedicated to Efim Zelmanov's 60th birthday”, Bento Gonçalves (Brazil; December 13-19, 2015).
Reductive homogeneous spaces and nonassociative algebras. Notes for a mini-course at the CIMPA research school “Géométrie différentielle et algèbres non associatives”, Marrakech (April 13-24, 2015).
Otros números (Spanish); Cincuentenario de la Olimpiada Matemática Española, Universidad Complutense de Madrid. November 21, 2014.
An English version, under the title Octonions, was delivered at the “Universidad Internacional Menéndez Pelayo” (Santander, July 9, 2015).
Graded modules over classical simple Lie algebras; XII Jornadas de Álgebra No Conmutativa, Málaga, April 2014, and Enveloping Algebras and Representation Theory, St. John's (Canada), August-September 2014.
Fine gradings and gradings by root systems on simple Lie algebras; Third Mile High Conference on Nonassociative Mathematics, August 2013 (University of Denver, USA), Groups, Nonassociative Algebras and Combinatorics, September-October 2013 (CIRM, Luminy, France), and Infinite Dimensional Lie Superalgebras and Their Representations, May 2016 (IPM Isfahan, Iran).
Some simple modular Lie superalgebras; Bicocca - Workshop on Lie Algebras 2013 (in honor of Professor Helmut Strade on the occasion of his 70th birthday). May 2013 (Milan, Italy).
Symmetric composition algebras and exceptional simple Lie algebras; Colloquium Talk (Uppsala Universitet, Sweden). December 2012.
A Freudenthal-Tits Supermagic Square; DAG days: "The Freudenthal-Tits Magic Square" (University of Ghent, Belgium), and Centro de Matemática da Universidade da Beira Interior (Covilhã, Portugal). October 2012.
Gradings on the Octonions, the Albert algebra, and exceptional simple Lie algebras; Groups, Rings, Lie and Hopf Algebras III (Memorial University of Newfoundland, Bonne Bay, NL, Canada). August 2012.
Gradings on the Octonions and the Albert algebra; Workshop on Exceptional Algebras and Groups (Ottawa, Canada). April 2012.
The Albert algebra as a twisted group algebra; International Conference on Ring Theory (dedicated to the 90th anniversary of A.I.Shirshov; Sobolev Institute of Mathematics, Novosibirsk, Russia), July 2011, and Nonassociative Algebra in Action: Past, Present, and Future Perspectives (in honor of Kevin McCrimmon; University of Virginia, USA), September 2011.
Gradings on simple Lie algebras; Mini-course given at the Conference "Non-Associative Algebras and Related Topics" (Coimbra, Portugal). July 2011.
Flexible composition algebras; International Conference in Memory of Hyo Chul Myung (KIAS, Seoul, Korea). April 2011.
Gradings on simple Lie algebras; University of Lund (Sweden) and First Joint Meeting of the American Mathematical Society and Sociedad de Matemática de Chile (Pucón, Chile). December 2010.
Composition algebras and their gradings; Universidad de Málaga (2010).
(This mini-course expands the one given in St. John's in 2009 under the same title.)
Jordan gradings on exceptional simple Lie algebras; Conference Algebras, Representations and Applications (Lie and Jordan Algebras, their Representations and Applications IV; Manaus, Brazil, 2009).) (Click here to see a picture.)
Composition algebras and their gradings; Atlantic Algebra Center minicourse, Memorial University of Newfoundland (St. John's, 2009).
Simple modular Lie superalgebras; Encuentro Matemático Hispano-Marroquí (Casablanca, 2008).
Números excepcionales; Seminario Vidal Abascal, Universidad de Santiago de Compostela (2008). (French version: Nombres exceptionnels, delivered at the Université de Pau et des Pays de l'Adour in 2008. English version: Exceptional Numbers, delivered at the Memorial University of Newfoundland in 2009.)
Gradings on composition algebras; Memorial University of Newfoundland (St. John's, 2008).
A Freudenthal Supermagic Square; University of California Lie Theory Workshop. A conference in honor of Professor Georgia Benkart (San Diego, 2008).
Tits construction, Freudenthal Magic Square, and modular simple Lie superalgebras; Lie Algebras and their Applications (Seoul, 2007).
Symmetry of the Tits construction of the exceptional simple Lie algebras; Primer Congreso Hispano-Francés de Matemáticas - Premier Congrès Franco-Espagnol de Mathématiques (Zaragoza, 2007).
An extended Freudenthal Magic Square in characteristic 3; From Lie Algebras to Quantum Groups (Coimbra, 2006).
Algunos objetos excepcionales; discurso de ingreso en la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza (February 23, 2006). (You may download the presentation too.)
New simple Lie superalgebras in characteristic 3; CIMMA (Almería, 2005).
Lie algebras with S₄ action and structurable algebras; Workshop on Nonassociative Algebras (Fields Institute, Toronto, 2005)
Otros números; Festividad de San Alberto Magno, Facultad de Ciencias de la Universidad de Zaragoza, (November 15, 2004). (You can check here how formal I am while lecturing.)
Symmetric composition algebras and Freudenthal's Magic Square; Lie and Jordan algebras, their representations and applications II (Guarujá, Brazil, 2004).
Productos vectoriales (Vector cross products); Seminario Rubio de Francia (Universidad de Zaragoza, 2004).
Tits construction and Freudenthal's Magic Square; Lie Algebras and Related Topics (KIAS, Seoul, Korea, 2003).
Nonassociative systems and irreducible homogeneous spaces; The Sixth International Workshop on Differential Geometry and Its Applications and The Third German-Romanian Seminar on Geometry (Cluj-Napoca, Romania, 2003).
A modified signed Brauer algebra as centralizer algebra of the unitary group; 2002 AMS Fall Central Section Meeting (Madison, WI, USA, 2002).
Exceptional Lie superalgebras; Lie and Jordan algebras; their representations and applications (Guarujá, Brazil, 2002).

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Last update: September 15, 2025