【摘要】 讨论了作为李代数、李超代数、ε李代数的推广的一类广义李代数:τ 李代数以及τ 李代数L上的普遍包络代数U.为了进一步说明U的结构,定义了与U相关的分次结合代数G及L上的分次结合代数:τ 对称代数S,并通过构造τ 李代数L的一个表示ψ,把关于李代数的普遍包络代数的重要结果———PBW定理,推广到τ 李代数上,得到了τ 李代数的PBW定理:分次结合代数G与S是同构的.更多还原

【Abstract】 This paper discussed a class of generalized Lie algebra:τ-Lie algebras, which are the generalization of the Lie algebras, the Lie superalgebras and the ε Lie algebras , and then introduced the conceptions of the enveloping algebra of a L, graded associative algebras G (which is correlative to L) and the τ-symmetric algebra S. By using the representation technique, the well-known PBW theorem of Lie algebras-"there exists an isomorphism of algebras between the graded associative algebras S and G"-is generalized to the τ-Lie algebras.更多还原