On symmetric invariants of centralisers in reductive Lie algebras

Panyushev, D. and Premet, A. and Yakimova, O. (2007) On symmetric invariants of centralisers in reductive Lie algebras. Journal of Algebra, 313 (Specia). pp. 343-391. ISSN 0021-8693

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Let g be a finite-dimensional simple Lie algebra of rank l over an algebraically closed field of characteristic 0. Let e be a nilpotent element of g and let q be the centraliser of e in g. In this paper we study the algebra S(q)^q of symmetric invariants of q. We prove that if g is of type A or C, then S(q)^q is always a graded polynomial algebra in l variables, and we show that this continues to hold for some nilpotent elements in the Lie algebras of other types. In type A we prove that the invariant algebra S(q)q is freely generated by a regular sequence in S(q) and describe the tangent cone at e to the nilpotent variety of g.

Item Type: Article
Uncontrolled Keywords: nilpotent elements, symmetric invariants
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
Depositing User: Professor Alexander Premet
Date Deposited: 31 Jan 2008
Last Modified: 20 Oct 2017 14:12
URI: https://eprints.maths.manchester.ac.uk/id/eprint/704

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