Second Cohomology of q-deformed Witt superalgebras

TL;DR

This paper computes the second cohomology group of q-deformed Witt superalgebras, revealing new insights into their algebraic structure by using q-deformation techniques and Hom-Lie superalgebra theory.

Contribution

It provides the first explicit calculation of the second cohomology group for q-deformed Witt superalgebras, extending the understanding of their deformation theory.

Findings

Second cohomology group computed explicitly

Identifies structure of q-deformed Witt superalgebras

Advances understanding of Hom-Lie superalgebra cohomology

Abstract

The purpose of this paper is to compute the second adjoint cohomology group of q-deformed Witt superalgebras. They are Hom-Lie superalgebras obtained by q-deformation of Witt Lie superalgebra, that is one considers $\sigma$-derivations instead of classical derivations.