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

 

Pi-envelopes of Lie superalgebras


Authors: Yuri Bahturin and Susan Montgomery
Journal: Proc. Amer. Math. Soc. 127 (1999), 2829-2839
MSC (1991): Primary 17A70, 16W50
Published electronically: April 23, 1999
MathSciNet review: 1600092
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Abstract: In this paper we find necessary and sufficient conditions on a finite-dimensional Lie superalgebra under which any associative PI-envelope of $L$ is finite-dimensional. We also extend M. Scheunert's result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.


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Additional Information

Yuri Bahturin
Affiliation: Department of Algebra, Moscow State University, 119899 Moscow, Russia
Email: bahturin@mech.math.msu.su

Susan Montgomery
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113
Email: smontgom@math.usc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04825-X
PII: S 0002-9939(99)04825-X
Received by editor(s): May 27, 1997
Received by editor(s) in revised form: December 11, 1997
Published electronically: April 23, 1999
Additional Notes: The authors were supported by NSF grant DMS-9500649
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society