Research:

Publications (since 2000)  |   Preprints  |   Talks


Publications:

  • 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. (Preprint of the 'Seminario García Galdeano'.)
  • 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.

top


Preprints:

  • Order 3 elements in G2 and idempotents in symmetric composition algebras; to appear in Canadian J. Math. (Preprint arXiv:1705.01293.)
  • On Kac's Jordan superalgebra (with A.S. Córdova-Martínez and Abbas Darehgazani); arXiv:1701.06798.
  • Cross products, invariants, and centralizers (with G. Benkart); to appear in J. Algebra. (Preprint arXiv:1606.07588.)

top


Talks:

top


Last update: October 9, 2017