n次微分分次Poisson代数的泛包络代数  

The universal enveloping algebras of n-differential graded Poisson algebras

作　　者：朱卉[1] 吴学超[1] 陈淼森[1] 

机构地区：[1]浙江师范大学数学系,浙江金华321004

出　　处：《浙江大学学报（理学版）》2016年第3期253-256,263,共5页Journal of Zhejiang University（Science Edition）

摘　　要：给出了n次微分分次Poisson代数的泛包络代数的定义及相关性质,同时给出了它的应用,即e是n次微分Z-分次Poisson代数范畴到微分Z-分次代数范畴的一个共变函子和(A^e)^(op)=(A^(op))~e,其中A是任意的n次微分分次Poisson代数.In order to study more extensively about Poisson algebras,this paper presents the definition and some properties of universal enveloping algebras of n-differential graded Poisson algebras and proves that universal enveloping algebras of n-differential graded Poisson algebras are differential graded algebras.During the study of the universal enveloping algebras of n-differential graded Poisson algebras,we find many interesting results.As applications,we prove that eis a covariant functor from the category of n-differential Z-graded Poisson algebras to the category of differential Z-graded algebras and（A^e）^op=（A^op）^e,for any n-differential graded Poisson algebras A.

关 键 词：分次Poisson代数 泛包络代数 微分分次代数映射 微分分次李代数映射 共变函子 

分 类 号：O154.2[理学—数学]