Simplicity of the Lie superalgebra of vector fields

TL;DR

This paper proves that for a finitely generated integral super domain, the Lie superalgebra of super derivations is simple, highlighting fundamental structural properties of these algebraic objects.

Contribution

It establishes the simplicity of the Lie superalgebra of super derivations for finitely generated integral super domains, a key structural result.

Findings

Lie superalgebra of super derivations is simple

Applicable to finitely generated integral super domains

Advances understanding of superalgebra structures

Abstract

For a finitely generated integral super domain $A$, we prove the Lie superalgebra $\mathcal{V} = Der(A)$ of super derivations is a simple Lie superalgebra.