On cohomology of filiform Lie superalgebras

TL;DR

This paper computes the Betti numbers and describes the cohomology algebra structures of model and low-dimensional filiform Lie superalgebras over algebraically closed fields, advancing understanding of their cohomological properties.

Contribution

It determines Betti numbers and cohomology algebra structures for model and certain low-dimensional filiform Lie superalgebras, providing new explicit descriptions.

Findings

Betti numbers for the model filiform Lie superalgebra are computed.

Explicit cohomology algebra structures are described for some low-dimensional cases.

The associative superalgebra of cohomology is decomposed for the model algebra.

Abstract

Suppose the ground field $\mathbb{F}$ is an algebraically closed field of characteristic different from 2, 3. We determine the Betti numbers and make a decomposition of the associative superalgebra of the cohomology for the model filiform Lie superalgebra. We also describe the associative superalgebra structures of the (divided power) cohomology for some low-dimensional filiform Lie superalgebras.