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Irreducible bimodules over alternative algebras and superalgebras


Authors: Ivan Shestakov and Maria Trushina
Journal: Trans. Amer. Math. Soc. 368 (2016), 4657-4684
MSC (2010): Primary 17A60, 17A70, 17D05; Secondary 16D90, 16D60
Published electronically: November 16, 2015
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Abstract: The aim of the paper is to describe irreducible birepresentations of alternative algebras and superalgebras. The complete classification is obtained for irreducible even bimodules of arbitrary dimension and characteristic and for finite-dimensional irreducible superbimodules over an algebraically closed field. We also describe irreducible superbimodules of any dimension and characteristic over the simple alternative superalgebras.


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Additional Information

Ivan Shestakov
Affiliation: Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010-CEP 05508-090, São Paulo, Brazil

Maria Trushina
Affiliation: Institute of Mathematics, Informatics and Natural Sciences, Moscow City Pedagogical University, ul. Sheremetevskaya, 29, Moscow, 129226, Russia

DOI: https://doi.org/10.1090/tran/6475
Received by editor(s): January 12, 2014
Received by editor(s) in revised form: May 13, 2014
Published electronically: November 16, 2015
Additional Notes: The first author was supported by FAPESP, Proc.2010/50347-9 and CNPq, Proc.3305344/ 2009-9
The second author was supported by FAPESP, Proc.2008/50141-1
Article copyright: © Copyright 2015 American Mathematical Society