On the center and semi-center of enveloping algebras in prime characteristic

JOURNAL OF ALGEBRA

卷:322

Article

Braun, Arniram¹  Vernik, Gil¹ 

[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

关键词: Enveloping algebra;    Lie algebra;    Semi-center;    Unique factorization;    Divisor class group;   

DOI  :  10.1016/j.jalgebra.2009.06.012

来源: Elsevier

【 摘 要 】

Theorems of J. Dixmier and C. Moeglin on the semi-center of enveloping algebras in zero characteristic and of R.P. Stanley and H. Nakajima on polynomial relative invariants of finite groups, are shown to have analogs for enveloping algebras and for Lie algebra polynomial invariants, in the prime characteristic case. We shall illustrate by examples the extent of these analogies. A key result is the realization of the semi-center as a fixed ring of the action of a finite set of nilpotent derivations on the center of an enveloping algebra of a related Lie algebra. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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