On Dixmier-Duflo isomorphism in positive characteristic - The classical nilpotent case

JOURNAL OF ALGEBRA

卷:382

Article

Ben-Shimol, Oz

关键词: Enveloping algebras;    Positive characteristic;    Duflo isomorphism;    Classical Lie algebras;   

DOI  :  10.1016/j.jalgebra.2013.02.021

来源: Elsevier

【 摘 要 】

Let g be the nil radical of the Borel subalgebra of one of the classical simple Lie algebras over a field F of characteristic p >= 0. For p > 0 we find an explicit realization of the center Z(g) of the enveloping algebra U(g) by generators and relations. This constructive approach yields an explicit isomorphism between Z(g) and the polynomial invariants algebra S(g)g. While realizing Z(g), we also prove that Z(g) is a complete intersection ring. Moreover, it leads to an explicit realization of Z(g) and S(g)(g) for p'=0 as well. This extends a result of Dixmier in type A(n). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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