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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Representations of exceptional simple alternative superalgebras of characteristic 3


Authors: M. C. López-Díaz and Ivan P. Shestakov
Journal: Trans. Amer. Math. Soc. 354 (2002), 2745-2758
MSC (2000): Primary 17D05, 17A70, 17C70
Published electronically: March 7, 2002
MathSciNet review: 1895201
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Abstract: We study representations of simple alternative superalgebras $B(1,2)$ and $B(2,4)$. The irreducible bimodules and bimodules with superinvolution over these superalgebras are classified, and some analogues of the Kronecker factorization theorem are proved for alternative superalgebras that contain $B(1,2)$ and $B(4,2)$.


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Additional Information

M. C. López-Díaz
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo, s/n, 33007, Oviedo, Spain
Email: cld@pinon.ccu.uniovi.es

Ivan P. Shestakov
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 - CEP 05315-970, São Paulo, Brasil; Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
Email: shestak@ime.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02993-8
PII: S 0002-9947(02)02993-8
Keywords: Alternative superalgebra and superbimodule, superinvolution, factorization theorem
Received by editor(s): April 17, 2001
Published electronically: March 7, 2002
Additional Notes: The first author was supported by FAPESP 2000/03404-5 and FICYT PB-PGI 99-04
The second author was supported by CNPq grant 300528/99-0
Article copyright: © Copyright 2002 American Mathematical Society