LPNG代数的泛中心扩张(英文）  

Universal Central Extensions of LPNG Algebras

作　　者：王春月[1] 张庆成[2] 魏竹[2] 张程程[2] 

机构地区：[1]吉林工程技术师范学院应用理学院,长春吉林130052 [2]东北师范大学数学与统计学院,长春吉林130024

出　　处：《数学进展》2014年第1期12-26,共15页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10871057,No.11171055)

摘　　要：利用交换结合代数,Lie代数和Novikov代数可以定义LPNG代数.LPNG代数具有三个代数结构,满足四个相容条件,并且可以分别构成Novikov-Poisson代数和Gel'fandDorfman代数.同时,通过对LPNG代数的中心扩张和泛中心扩张的研究,得出LPNG代数有泛中心扩张的充分必要条件是LPNG代数是完备的.最后,得到了自同态和导子提升条件.LPNG algebras are defined on the basis of commutative associative algebras, Lie algebras and Novikov algebras. This class of algebras has three algebraic structures, satisfies four compatible conditions, and can construct Novikov-Poisson algebras and Gel＇fand-Dorfman algebras. Meanwhile, through studying the central extensions and universal central extensions of LPNG algebras, we obtain that an LPNG algebra has a universal central extension if and only if it is perfect. In the last section we acquire the conditions of lifting automorphisms and derivations.

关 键 词：LPNG代数 泛中心扩张 导子 自同态 

分 类 号：O152.5[理学—数学]