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

 

On identities of infinite dimensional Lie superalgebras


Authors: Dušan Repovš and Mikhail Zaicev
Journal: Proc. Amer. Math. Soc. 141 (2013), 4139-4153
MSC (2010): Primary 17C05, 16P90; Secondary 16R10
Published electronically: August 15, 2013
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Abstract: We study codimension growth of infinite dimensional Lie super-
algebras over an algebraically closed field of characteristic zero. We prove that if a Lie superalgebra $ L$ is a Grassmann envelope of a finite dimensional simple Lie algebra, then the PI-exponent of $ L$ exists and is a positive integer.


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Additional Information

Dušan Repovš
Affiliation: Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, Kardeljeva Pl. 16, Ljubljana, 1000 Slovenia
Email: dusan.repovs@guest.arnes.si

Mikhail Zaicev
Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992 Russia
Email: zaicevmv@mail.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11691-6
PII: S 0002-9939(2013)11691-6
Keywords: Polynomial identity, Lie algebra, codimension, exponential growth
Received by editor(s): April 17, 2011
Received by editor(s) in revised form: December 9, 2011, January 4, 2012, and February 8, 2012
Published electronically: August 15, 2013
Additional Notes: The first author was supported by the Slovenian Research Agency grants P1-0292-0101 and J1-4144-0101
The second author was partially supported by RFBR grant No. 13-01-00234a
Both authors thank the referee for several comments and suggestions
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2013 American Mathematical Society