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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Codimensions of polynomial identities of representations of Lie algebras


Author: A. S. Gordienko
Journal: Proc. Amer. Math. Soc. 141 (2013), 3369-3382
MSC (2010): Primary 17B01; Secondary 16R10, 17B10, 20C30
Published electronically: June 18, 2013
MathSciNet review: 3080160
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Abstract: Consider a representation $ \rho \colon L \to \mathfrak{gl}(V)$ where $ L$ is a Lie algebra and $ V$ is a finite dimensional vector space. We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial identities of $ \rho $.


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Additional Information

A. S. Gordienko
Affiliation: Memorial University of Newfoundland, St. John’s, NL, Canada
Email: alexey.gordienko@vub.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11622-9
PII: S 0002-9939(2013)11622-9
Keywords: Lie algebra, polynomial identity, codimension, cocharacter, symmetric group, Young diagram
Received by editor(s): June 17, 2011
Received by editor(s) in revised form: December 15, 2011
Published electronically: June 18, 2013
Additional Notes: This work was supported by postdoctoral fellowships from the Atlantic Association for Research in Mathematical Sciences (AARMS), the Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and the Natural Sciences and Engineering Research Council of Canada (NSERC)
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.