Group gradings on simple Lie algebras in positive characteristic
نویسندگان
چکیده
منابع مشابه
Group Gradings on Simple Lie Algebras in Positive Characteristic
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 = 2: sln(F ) (n not divisible by p), son(F ) (n ≥ 5, n = 8) and spn(F ) (n ≥ 6, n even).
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In this paper we consider gradings by a finite abelian group G on the Lie algebra sln(F ) over an algebraically closed field F of characteristic different from 2 and not dividing n.
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2 Kac coordinates 5 2.1 Based automorphisms and affine root systems . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Torsion points, Kac coordinates and the normalization algorithm . . . . . . . . . . . . 9 2.3 μm-actions on Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Principal μm-actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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The fine abelian group gradings on the simple classical Lie algebras (including D4) over algebraically closed fields of characteristic 0 are determined up to equivalence. This is achieved by assigning certain invariant to such gradings that involve central graded division algebras and suitable sesquilinear forms on free modules over them.
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Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09634-2