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

   

 

Simple $ G$-graded algebras and their polynomial identities


Authors: Eli Aljadeff and Darrell Haile
Journal: Trans. Amer. Math. Soc. 366 (2014), 1749-1771
MSC (2010): Primary 16R50, 16R10, 16W50
Published electronically: November 14, 2013
MathSciNet review: 3152711
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be any group and $ F$ an algebraically closed field of characteristic zero. We show that any $ G$-graded finite dimensional associative $ G$-simple algebra over $ F$ is determined up to a $ G$-graded isomorphism by its $ G$-graded polynomial identities. This result was proved by Koshlukov and Zaicev in case $ G$ is abelian.


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Additional Information

Eli Aljadeff
Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Darrell Haile
Affiliation: Department of Mathematics, Indiana University, 831 E 3rd Street, Bloomington, Indiana 47405

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05842-4
Keywords: Graded algebra, polynomial identity
Received by editor(s): November 25, 2011
Received by editor(s) in revised form: March 31, 2012
Published electronically: November 14, 2013
Additional Notes: The first author was supported by the Israel Science Foundation (grant No. 1017/12)
Article copyright: © Copyright 2013 American Mathematical Society