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

DOI:
https://doi.org/10.1090/S0002-9939-08-09634-2

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

MR Author ID:
202355

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

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