Maurer-Cartan characterization, cohomology and deformations of equivariant Lie superalgebras

TL;DR

This paper develops Maurer-Cartan characterizations and introduces equivariant cohomology and deformation theory for Lie superalgebras, providing new tools to study their structure and extensions.

Contribution

It introduces equivariant cohomology and deformation theory for Lie superalgebras, and characterizes equivariant central extensions using second equivariant cohomology.

Findings

Maurer-Cartan characterizations of equivariant Lie superalgebras

Development of equivariant cohomology and deformation theory

Examples of equivariant deformations of classical Lie superalgebras

Abstract

In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. We introduce equivariant cohomology and equivariant formal deformation theory of Lie superalgebras. As an application of equivariant cohomology we study the equivariant formal deformation theory of Lie superalgebras. As another application we characterize equivariant central extensions of Lie superalgebras using second equivariant cohomology. We give some examples of Lie superalgebras with an action of a group and equivariant formal deformations of a classical Lie superalgebras.