Integral Bases for the Universal Enveloping Superalgebras of Map Superalgebras II

TL;DR

This paper constructs explicit integral bases for the universal enveloping superalgebras of map superalgebras derived from Cartan type complex Lie superalgebras, advancing the understanding of their algebraic structure.

Contribution

It introduces integral forms and provides explicit bases for these forms in the context of map superalgebras of Cartan type Lie superalgebras.

Findings

Explicit integral bases for the universal enveloping superalgebras are constructed.

Integral forms for these superalgebras are defined and characterized.

The work extends the theory of integral bases to a new class of superalgebras.

Abstract

In this paper we define integral forms for the universal enveloping superalgebras of the map superalgebras of Cartan type complex Lie superalgebras, and exhibit explicit integral bases for these integral forms.