Universal Enveloping Algebras of Poisson SuperalgebrasUniversal Enveloping Algebras of Poisson SuperalgebrasT. Lamkin

被引：0
|
作者：
Thomas Lamkin [1 ]
机构：
[1] Miami University,Department of Mathematics
[2] UCSD,Department of Mathematics (Current)
来源：
Algebras and Representation Theory | 2025年 / 28卷 / 1期
关键词：
Poisson superalgebra; Enveloping algebra; Lie-Rinehart superalgebra; PBW Theorem; 17B63; 17B60; 17B35; 16T05;
D O I：
10.1007/s10468-024-10312-7
中图分类号：
学科分类号：
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：34
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