# Mixed cohomology of Lie superalgebras

## TL;DR

This paper introduces a novel cohomology theory for Lie superalgebras, combining differential and integral forms, and demonstrates its relation to standard cohomology with computed examples.

## Contribution

It develops a new cohomology framework for Lie superalgebras using a BRST complex and Weyl superalgebra, extending existing theories.

## Key findings

- New cohomology includes standard Lie superalgebra cohomology as a special case
- Explicit computations of new cohomology groups are provided
- The framework involves a BRST complex and inequivalent representations of the Weyl superalgebra

## Abstract

We investigate a new cohomology of Lie superalgebras, which may be compared to a de Rham cohomology of Lie supergroups involving both differential and integral forms. It is defined by a BRST complex of Lie superalgebra modules, which is formulated in terms of a Weyl superalgebra and incorporates inequivalent representations of the bosonic Weyl subalgebra. The new cohomology includes the standard Lie superalgebra cohomology as a special case. Examples of new cohomology groups are computed.