Integral bases for the universal enveloping algebras of map superalgebras

TL;DR

This paper constructs an explicit integral basis for the universal enveloping algebra of map superalgebras formed from finite-dimensional simple classical Lie superalgebras and commutative associative algebras over complex numbers.

Contribution

It introduces an integral form for the universal enveloping algebra of map superalgebras and provides an explicit basis for this integral form.

Findings

Explicit integral basis for the universal enveloping algebra of map superalgebras

Construction of an integral form for these algebras

Foundation for further algebraic and representation-theoretic studies

Abstract

Let $\mathfrak{g}$ be a finite dimensional complex simple classical Lie superalgebra and $A$ be a commutative, associative algebra with unity over $\mathbb{C}$. In this paper we define an integral form for the universal enveloping algebra of the map superalgebra $\mathfrak{g}\otimes A$, and exhibit an explicit integral basis for this integral form.