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浙江大学学报(理学版)  2016, Vol. 43 Issue (3): 253-256    DOI: 10.3785/j.issn.1008-9497.2016.03.001
数学与计算机科学     
n次微分分次Poisson代数的泛包络代数
朱卉, 吴学超, 陈淼森
浙江师范大学 数学系, 浙江 金华 321004
The universal enveloping algebras of n-differential graded Poisson algebras
ZHU Hui, WU Xuechao, CHEN Miaosen
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang Province, China
 全文: PDF(710 KB)  
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en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(Ae)op=(Aop)e,其中A是任意的n次微分分次Poisson代数.
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    
Abstract: 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 e is a covariant functor from the category of n-differential Z-graded Poisson algebras to the category of differential Z-graded algebras and (Ae)op=(Aop)e, for any n-differential graded Poisson algebras A.
Key words: graded Poisson algebras    universal enveloping algebras    differential graded algebra map    differential graded Lie algebra map    covariant functor
收稿日期: 2015-12-21 出版日期: 2016-03-01
CLC:  O154.2  
通讯作者: 陈淼森,E-mail:mschen@zjnu.cn.     E-mail: mschen@zjnu.cn
作者简介: 朱卉(1991-),ORCID:http://orcid.org/0000-0001-9888-6740,女,硕士研究生,主要从事代数学研究.
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朱卉, 吴学超, 陈淼森. n次微分分次Poisson代数的泛包络代数[J]. 浙江大学学报(理学版), 2016, 43(3): 253-256.

ZHU Hui, WU Xuechao, CHEN Miaosen. The universal enveloping algebras of n-differential graded Poisson algebras. Journal of Zhejiang University (Science Edition), 2016, 43(3): 253-256.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.03.001        https://www.zjujournals.com/sci/CN/Y2016/V43/I3/253

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