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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## Abstract

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 |
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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: | http://eprints.maths.manchester.ac.uk/id/eprint/704 |

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