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Unital bimodules over the simple Jordan superalgebra $ D(t)$

Author(s): Consuelo Martínez; Efim Zelmanov
Journal: Trans. Amer. Math. Soc. 358 (2006), 3637-3649.
MSC (2000): Primary 17C70
Posted: December 21, 2005
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Abstract | References | Similar articles | Additional information

Abstract: We classify indecomposable finite dimensional bimodules over Jordan superalgebras $ D(t)$, $ t \neq -1,0,1$.

References:

[J1]
N. Jacobson, Structure and Representation of Jordan algebras, Amer. Math. Soc., Providence, R.I., (1969). MR 0251099 (40:4330)

[J2]
N. Jacobson, Lie Algebras, Dover Publications, Inc., New York, (1979); Republication of the 1962 original. MR 0559927 (80k:17001)

[J3]
N. Jacobson, General representation theory of Jordan algebras, Trans. Amer. Math. Soc. 70, 509-530, (1951). MR 0041118 (12:797d)

[K1]
V. G. Kac, Lie Superalgebras, Advances in Mathematics 26, 8-96, (1977). MR 0486011 (58:5803)

[K2]
V. G. Kac, Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras, Comm. in Algebra 5 (13), 1375-1400, (1977). MR 0498755 (58:16806)

[Ka1]
I. L. Kantor, Connection between Poisson brackets and Jordan and Lie superalgebras, Lie theory, differential equations and representation theory, 213-225, Montreal (1989). MR 1121965 (92f:17040)

[Ka2]
I. L. Kantor, Jordan and Lie superalgebras defined by a Poisson algebra, Algebra and Analysis, 55-80. Amer. Math. Soc. Transl. Ser. (2), 151, (1992). MR 1191172 (93j:17004)

[Kp1]
I. Kaplansky, Superalgebras, Pacific J. of Math. 86, 93-98, (1980). MR 0586871 (81j:17006)

[Kp2]
I. Kaplansky, Graded Jordan Algebras I, Preprint.

[MZ]
C. Martínez and E. Zelmanov, Specializations of Jordan Superalgebras, Canad. Math. Bull. 45 (4), 653-671, (2002). MR 1941232 (2003k:17040)

[ZSSS]
K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov and A. I. Shirshov, Rings that are nearly associative, Academic Press, New York, 1982. MR 0668355 (83i:17001)

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Additional Information:

Consuelo Martínez
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo, s/n, 33007 Oviedo, Spain

Efim Zelmanov
Affiliation: Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 -- and -- KIAS, Seoul 130-012, South Korea

DOI: 10.1090/S0002-9947-05-03821-3
PII: S 0002-9947(05)03821-3
Received by editor(s): December 15, 2003
Received by editor(s) in revised form: August 18, 2004 and August 28, 2004
Posted: December 21, 2005
Additional Notes: The first author was partially supported by BFM 2001-3239-C03-01 and FICYT PR-01-GE-15
The second author was partially supported by NSF grant DMS-0071834
Copyright of article: Copyright 2005, American Mathematical Society

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