Hochschild cohomology of symmetric groups in low degrees

TL;DR

This paper calculates the dimensions of Hochschild cohomology for symmetric groups over prime fields in low degrees, involving partition identities and generating functions.

Contribution

It provides explicit computations of Hochschild cohomology dimensions for symmetric groups in low degrees, a novel contribution to the understanding of their algebraic structure.

Findings

Dimensions of Hochschild cohomology are explicitly computed in low degrees.

Partition identities and generating functions are used to analyze cohomology.

Results enhance understanding of symmetric groups' algebraic properties.

Abstract

We compute the dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the Hochschild cohomology of symmetric groups.