Group gradings on simple Lie algebras in positive characteristic
Authors:
Yuri Bahturin, Mikhail Kochetov and Susan Montgomery
Journal:
Proc. Amer. Math. Soc. 137 (2009), 12451254
MSC (2000):
Primary 16W10, 16W50, 17B50, 17B70
Published electronically:
October 20, 2008
MathSciNet review:
2465646
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: In this paper we describe all gradings by a finite abelian group on the following Lie algebras over an algebraically closed field of characteristic : ( not divisible by ), (, ) and (, even).
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 1.
 Bahturin, Y.; Goze, M. symmetric spaces, Pacific J. Math., 236 (2008), 121.
 2.
 Bahturin, Y.; Giambruno, A. Group gradings on associative algebras with involution, Canad. Math. Bull., 51 (2008), 182194.
 3.
 Bahturin, Y.; Shestakov, I.; Zaicev, M. Gradings on simple Jordan and Lie algebras, J. Algebra, 283 (2005), 849868. MR 2111225 (2005i:17038)
 4.
 Bahturin, Y.; Zaicev, M. Involutions on graded matrix algebras, J. Algebra, 315 (2007), 527540. MR 2351876
 5.
 Bahturin, Y.; Zaicev, M. Graded algebras and graded identities, Polynomial identities and combinatorial methods (Pantelleria, 2001), 101139, Lecture Notes in Pure and Appl. Math., 235, Dekker, New York, 2003. MR 2021796 (2005a:16059)
 6.
 Bahturin, Y.; Zaicev, M. Gradings on simple Lie algebras of type ``A'', J. Lie Theory, 16 (2006), 719742. MR 2270657 (2007i:17037)
 7.
 Beidar, K. I.; Brešar, M.; Chebotar, M. A.; Martindale, W. S., 3rd. On Herstein's Lie map conjectures. III, J. Algebra, 249 (2002), no. 1, 5994. MR 1887985 (2003c:16042)
 8.
 Benkart, G.; Gregory, T.; Premet, A. The recognition theorem for graded Lie algebras in prime characteristic, arXiv:math.RA/0508373 v2 (29 Sep 2005).
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 Blau, P. S.; Martindale, W. S., 3rd. Lie isomorphisms in prime GPI rings with involution, Taiwanese J. Math., 4 (2000), 215252. MR 1757403 (2001i:16061)
 10.
 Dieudonné, J. Introduction to the theory of formal groups. Pure and Applied Mathematics, 20, Marcel Dekker, Inc., New York, 1973. MR 0332802 (48:11128)
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 Jantzen, J. C. Representations of algebraic groups. Second edition. Mathematical Surveys and Monographs, 107, American Math. Soc., Providence, RI, 2003. MR 2015057 (2004h:20061)
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 Kac, V. Graded algebras and symmetric spaces. Funct. Anal. Pril., 2 (1968), 9394. MR 0231944 (38:270)
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 Kac, V. Infinite dimensional Lie algebras, second edition, Cambridge University Press, 1985. MR 823672 (87c:17023)
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 Montgomery, S. Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, 82, American Math. Soc., Providence, RI, 1993. MR 1243637 (94i:16019)
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 Zelmanov, E. Lie algebras with a finite grading. Engl. Transl., Math. USSRSb., 52 (1985), 347385. MR 0752226
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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 900892532
Email:
smontgom@math.usc.edu
DOI:
http://dx.doi.org/10.1090/S0002993908096342
PII:
S 00029939(08)096342
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 # 22706004 and by a URP grant, Memorial University of Newfoundland.
The second author was supported by a Startup Grant, Memorial University of Newfoundland.
The third author was supported by NSF grant DMS 0401399.
Communicated by:
Birge HuisgenZimmermann
Article copyright:
© Copyright 2008
American Mathematical Society
