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
![[thumbnail of strel.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
strel.pdf Download (539kB) |
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 |
|---|---|
| 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 |
Actions (login required)
 |
View Item |