|
Representation theory of Jordan superalgebras I
Author(s):
Consuelo
Martínez;
Efim
Zelmanov
Journal:
Trans. Amer. Math. Soc.
362
(2010),
815-846.
MSC (2000):
Primary 17C70;
Secondary 17C55, 17B10, 17B60
Posted:
September 18, 2009
MathSciNet review:
2551507
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We complete the classification of irreducible bimodules over simple finite dimensional Jordan superalgebras.
References:
-
- 1.
- N. Jacobson, Structure and Representation of Jordan algebras, Amer. Math. Soc., Providence, R.I., 1969. MR 0251099 (40:4330)
- 2.
- V.G. Kac, Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras, Comm. in Algebra 5 (13) (1977), 1375-1400. MR 0498755 (58:16806)
- 3.
- I.L. Kantor, Jordan and Lie superalgebras defined by Poisson brackets, Algebra and Analysis, 55-79, 1989. Amer. Math. Soc. Transl. Ser. (2)151, 1992. MR 1191172 (93j:17004)
- 4.
- I. Kaplansky, Superalgebras, Pacific J. of Math. 86 (1980), 93-98. MR 586871 (81j:17006)
- 5.
- I. Kaplansky, Graded Jordan Algebras I, Preprint.
- 6.
- O. Loos, Jordan pairs, Lecture Notes in Mathematics, vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721 (56:3071)
- 7.
- C. Martınez and I. Shestakov, Unital irreducible bimodules over
, Preprint. - 8.
- C. Martınez, I. Shestakov and E. Zelmanov, Jordan algebras defined by brackets, J. London Math. Soc. (2) 64, no. 2 (2001), 357-368. MR 1853456 (2002g:17045)
- 9.
- C. Martınez, I. Shestakov and E. Zelmanov, Jordan bimodules over the superalgebras
and , Submitted - 10.
- C. Martınez and E. Zelmanov, Lie superalgebras graded by
and , Proc. Natl. Acad. Sci. USA 100 no.14 (2003), 8130-8137. MR 1989345 (2005c:17047) - 11.
- C. Martınez and E. Zelmanov, Specializations of Simple Jordan Superalgebras, Canad. Math. Bull. 45 (4) (2002), 653-671. MR 1941232 (2003k:17040)
- 12.
- C. Martınez and E. Zelmanov, Unital bimodules over the simple Jordan superalgebras
, Trans. Amer. Math. Soc. 358 no.8 (2006), 3637-3649. MR 2218992 (2007b:17048) - 13.
- C. Martınez and E. Zelmanov, Representation theory of Jordan superalgebras II, Preprint.
- 14.
- Y. Medveded and E. Zelmanov, Some counterexamples in the theory of Jordan Algebras, Nonassociative Algebraic Models, Nova Science Publish., S. González and H.C. Myung eds. (1992), 1-16. MR 1189608 (93m:17017)
- 15.
- N.A. Pisarenko, The structure of alternative superbimodules, Algebra and Logic 33 no.6 (1995), 386-397. MR 1347266 (96h:17042)
- 16.
- A.S. Shtern, Representation of an exceptional Jordan superalgebra, Funktzional Anal. i Prilozhen 21 (1987), 93-94. MR 911787 (89b:17009)
- 17.
- M. N. Trushina, Irreducible representations of a certain Jordan superalgebra, J. Algebra Appl. 4, no. 1 (2005), 1-14. MR 2130461 (2005k:17045)
- 18.
- C.T.C. Wall, Graded Brauer groups, J. Reine Angew Math. 213 (1964), 187-199. MR 0167498 (29:4771)
- 19.
- K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov and A. I. Shirshov, Rings that are rearly associative, Academic Press, New York, 1982. MR 668355 (83i:17001)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
17C70,
17C55, 17B10, 17B60
Retrieve articles in all Journals with
MSC (2000):
17C70,
17C55, 17B10, 17B60
Additional Information:
Consuelo
Martínez
Affiliation:
Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo, s/n, 33007 Oviedo, Spain
Email:
cmartinez@uniovi.es
Efim
Zelmanov
Affiliation:
Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
Email:
ezelmano@maths.ucsd.edu
DOI:
10.1090/S0002-9947-09-04883-1
PII:
S 0002-9947(09)04883-1
Keywords:
Jordan superalgebra,
Jordan bimodule
Received by editor(s):
December 19, 2007
Posted:
September 18, 2009
Additional Notes:
The first author was partially supported by MTM 2007-67884-C04-01 and FICYT IB-05-186.
The second author was partially supported by the NSF grants FRG DMS-0455906 and DMS-0500568.
Copyright of article:
Copyright
2009,
American Mathematical Society
|