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

 

Group gradings on simple Lie algebras in positive characteristic


Authors: Yuri Bahturin, Mikhail Kochetov and Susan Montgomery
Journal: Proc. Amer. Math. Soc. 137 (2009), 1245-1254
MSC (2000): Primary 16W10, 16W50, 17B50, 17B70
Published electronically: October 20, 2008
MathSciNet review: 2465646
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we describe all gradings by a finite abelian group $ G$ on the following Lie algebras over an algebraically closed field $ F$ of characteristic $ p\neq 2$: $ \mathfrak{sl} _n(F)$ ($ n$ not divisible by $ p$), $ \mathfrak{so}_n(F)$ ($ n\geq 5$, $ n\neq 8$) and $ \mathfrak{sp} _n(F)$ ($ n\geq 6$, $ n$ even).


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Additional Information

Yuri Bahturin
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C5S7, Canada
Email: yuri@math.mun.ca

Mikhail Kochetov
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C5S7, Canada
Email: mikhail@math.mun.ca

Susan Montgomery
Affiliation: Department of Mathematics, University of Southern California, 3620 South Vermont Avenue, KAP 108, Los Angeles, California 90089-2532
Email: smontgom@math.usc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09634-2
PII: S 0002-9939(08)09634-2
Received by editor(s): July 5, 2007
Received by editor(s) in revised form: February 8, 2008, and April 21, 2008
Published electronically: October 20, 2008
Additional Notes: The first author was partially supported by NSERC grant # 227060-04 and by a URP grant, Memorial University of Newfoundland.
The second author was supported by a Start-up Grant, Memorial University of Newfoundland.
The third author was supported by NSF grant DMS 0401399.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2008 American Mathematical Society