Universal Enveloping Algebras of Poisson Superalgebras

被引：0
|
作者：
Lamkin, Thomas [1 ,2 ]
机构：
[1] Miami Univ, Dept Math, 301 S Patterson Ave, Oxford, OH 45056 USA
[2] UCSD, Dept Math Current, 9500 Gilman Dr, La Jolla, CA 92093 USA
来源：
ALGEBRAS AND REPRESENTATION THEORY | 2025年 / 28卷 / 01期
关键词：
Poisson superalgebra; Enveloping algebra; Lie-Rinehart superalgebra; PBW Theorem; COHOMOLOGY;
D O I：
10.1007/s10468-024-10312-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we define and study the universal enveloping algebra of a Poisson superalgebra. In particular, a new PBW Theorem for Lie-Rinehart superalgebras is proved leading to a PBW Theorem for Poisson superalgebras, we show the universal enveloping algebra of a Poisson Hopf superalgebra (resp. Poisson-Ore extension) is a Hopf superalgebra (resp. iterated Ore extension), and we study the universal enveloping algebra for interesting classes of Poisson superalgebras such as Poisson symplectic superalgebras.
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页码：157 / 191
页数：35
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