Symmetry criteria for Hochschild extensions

TL;DR

This paper establishes precise symmetry criteria for Hochschild extensions of finite dimensional algebras, focusing on dual bimodules and Hochschild 2-cocycles, to determine when such extensions are symmetric algebras.

Contribution

It provides two necessary and sufficient conditions for Hochschild extensions to be symmetric algebras, advancing understanding of their structural properties.

Findings

Identifies conditions under which Hochschild extensions are symmetric

Provides a characterization involving Hochschild 2-cocycles

Enhances criteria for symmetry in algebra extensions

Abstract

We give two sufficient and necessary conditions for a Hochschild extension of a finite dimensional algebra by its dual bimodule and a Hochschild 2-cocycle to be a symmetric algebra.