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Title: Weyl Groups of Fine Gradings on Simple Lie Algebras of Types A, B, C and D
Authors: Elduque, Alberto
Kochetov, Mikhail
Keywords: Graded Algebra
Fine Grading
Weyl Group
Simple Lie Algebra
Issue Date: 2012
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 38, No 1-3, (2012), 7p-36p
Abstract: Given a grading Γ : L ⨁ = g ∈ G L g on a nonassociative algebra L by an abelian group G, we have two subgroups of Aut(L): the automorphisms that stabilize each component L g (as a subspace) and the automorphisms that permute the components. By the Weyl group of Γ we mean the quotient of the latter subgroup by the former. In the case of a Cartan decomposition of a semisimple complex Lie algebra, this is the automorphism group of the root system, i.e., the so-called extended Weyl group. A grading is called fine if it cannot be refined. We compute the Weyl groups of all fine gradings on simple Lie algebras of types A, B, C and D (except D 4) over an algebraically closed field of characteristic different from 2.
Description: 2010 Mathematics Subject Classification: Primary 17B70, secondary 17B40, 16W50.
ISSN: 1310-6600
Appears in Collections:Volume 38, Number 1-3

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