Structure of Weyl type Lie algebras

[摘要] Let A be a unital commutative associative algebra over a field F of characteristic zero, D a commutative subalgebra of Der(F)(A) (all derivations of the associative algebra A). We assume that A is D-simple and denote the center of the Weyl type algebra A[D] by F-1 which is an extension field of F when A[D] is simple. In this paper, it is proved that the simple associative algebras A[D] are noncommutative domains, and then the derivations of the simple associative algebras A[D] and of the associated Lie algebras A[D](L) re completely determined when dim(F1) F-1 D < infinity. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] Weyl type Lie algebras;derivations