Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The Kac Jordan superalgebra: automorphisms and maximal subalgebras


Authors: Alberto Elduque, Jesús Laliena and Sara Sacristán
Journal: Proc. Amer. Math. Soc. 135 (2007), 3805-3813
MSC (2000): Primary 17C70
DOI: https://doi.org/10.1090/S0002-9939-07-08938-1
Published electronically: September 7, 2007
MathSciNet review: 2341930
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note the group of automorphisms of the Kac Jordan superalgebra is described and used to classify the maximal subalgebras.


References [Enhancements On Off] (What's this?)

  • 1. A. Albert, On a certain algebra of quantum mechanics, Ann. of Math. (2) 35 (1934), 65-73. MR 1503142
  • 2. G. Benkart, A. Elduque, A new construction of the Kac Jordan superalgebra, Proc. Amer. Math. Soc. 130 (2002) no.11, 3209-3217. MR 1912998 (2003d:17024)
  • 3. E. Dynkin, Maximal subgroups of the classical groups, Trudy Moskov. Mat. Obsc., (1952), 39-166; Amer. Math. Soc. Transl. 6 (1957), 245-378. MR 0049903 (14:244d)
  • 4. E. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Mat. Sbornik 30 (1952), 249-462; Amer. Math. Soc. Transl. 6 (1957), 111-244. MR 0047629 (13:904c)
  • 5. A. Elduque, On maximal subalgebras of central simple Malcev algebras, J. Algebra 103 (1) (1986), 216-227. MR 860701 (88a:17043)
  • 6. A. Elduque, J. Laliena, S. Sacristán, Maximal subalgebras of associative superalgebras, J. Algebra 275 (2004), 40-58. MR 2047439 (2005c:16064)
  • 7. A. Elduque, J. Laliena, S. Sacristán, Maximal subalgebras of Jordan superalgebras, arXiv:math.RA/0606017
  • 8. P. Jordan, J. von Neumann and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math. (2) 35 (1934), 29-64. MR 1503141
  • 9. V.G. Kac, Classification of Simple Z-Graded Lie Superalgebras and Simple Jordan Superalgebras, Comm. Algebra 13 no.5 (1977), 1375-1400. MR 0498755 (58:16806)
  • 10. I.L. Kantor, Connection between Poisson brackets and Jordan and Lie superalgebras, Lie Theory, Differential Equations and Representation Theory. Publications CRM, Montreal, 1990, 213-225. MR 1121965 (92f:17040)
  • 11. D. King, The split Kac Superalgebra $ K_{10}$, Comm. Algebra 22 no.1 (1994), 29-40. MR 1255668 (95a:17014)
  • 12. K. McCrimmon, Speciality and Non-speciality of Two Jordan Superalgebras, J. Algebra 149 (1992), 326-351. MR 1172433 (93k:17060)
  • 13. Yu.A. Medvedev, E.I. Zelmanov, Some counterexamples in the theory of Jordan algebras, in: Nonassociative Algebraic Models (Zaragoza 1989), S. González and H.C. Myung, eds.; Nova Sci. Publ., Commack, NY, 1992, 1-16.
  • 14. M. Racine, On Maximal subalgebras, J. Algebra 30 (1974), 155-180. MR 0349771 (50:2264)
  • 15. M. Racine, Maximal subalgebras of exceptional Jordan algebras, J. Algebra 46 (1977), 12-21. MR 0450356 (56:8651)
  • 16. M.L. Racine, E.I. Zelmanov, Simple Jordan Superalgebras with Semisimple Even Part, J. Algebra 270 (2003), 374-444. MR 2019625 (2005b:17063)
  • 17. A.S. Shtern, Representation of an exceptional Jordan superalgebra, Funktsional Anal. i Prilozhen 21 (1987), 93-94 (Russian), English translation in Functional Anal. Appl. 21 (1987), 253-254. MR 911787 (89b:17009)
  • 18. C.T.C. Wall, Graded Brauer Groups, Jour. Reine Angew. Math. 213 (1964), 187-199. MR 0167498 (29:4771)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 17C70

Retrieve articles in all journals with MSC (2000): 17C70


Additional Information

Alberto Elduque
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: elduque@unizar.es

Jesús Laliena
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004, Logroño, Spain
Email: jesus.laliena@dmc.unirioja.es

Sara Sacristán
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004, Logroño, Spain
Email: ssacrist@barpimo.com

DOI: https://doi.org/10.1090/S0002-9939-07-08938-1
Keywords: Kac Jordan superalgebra, automorphism, maximal subalgebra
Received by editor(s): September 6, 2005
Received by editor(s) in revised form: September 26, 2006
Published electronically: September 7, 2007
Additional Notes: The first and second authors have been supported by the Spanish Ministerio de Educación y Ciencia and FEDER (MTM 2004-081159-C04-02). The first author also acknowledges support of the Diputación General de Aragón (Grupo de investigación de Álgebra)
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society