English

Universal Enveloping Algebras of Poisson Superalgebras

Rings and Algebras 2023-02-13 v3

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.

Keywords

Cite

@article{arxiv.2102.06895,
  title  = {Universal Enveloping Algebras of Poisson Superalgebras},
  author = {Thomas Lamkin},
  journal= {arXiv preprint arXiv:2102.06895},
  year   = {2023}
}

Comments

Reorganization of paper and further improvements to writing