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arXiv · 2102.06895

Universal Enveloping Algebras of Poisson Superalgebras

Thomas Lamkin
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Abstract

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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Thomas Lamkin. 2021-02-13. Universal Enveloping Algebras of Poisson Superalgebras. https://arxiv.org/abs/2102.06895

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