On the bosonization of the enveloping algebra of a finite dimensional Lie superalgebra

TL;DR

This paper explores the algebraic structure of bosonizations of enveloping algebras of Lie superalgebras, highlighting properties and presenting a PI Hopf algebra that is not finitely module over its center.

Contribution

It provides a survey of ring-theoretical properties of these bosonizations and introduces a novel PI Hopf algebra with unique module properties.

Findings

Identified a PI Hopf algebra not finitely generated over its center.

Surveyed key ring-theoretical properties of bosonizations of Lie superalgebra enveloping algebras.

Highlighted structural differences in algebraic properties of these bosonizations.

Abstract

We exhibit a PI Hopf algebra that is not a finite module over its center. We survey some ring-theoretical properties of the bosonizations of enveloping algebras of Lie superalgebras.