The ordinary quivers of Hochschild extension algebras for self-injective Nakayama algebras

TL;DR

This paper determines the structure of the ordinary quiver of Hochschild extension algebras for self-injective Nakayama algebras using Hochschild homology, providing explicit descriptions of their quivers.

Contribution

It explicitly describes the ordinary quiver of Hochschild extension algebras for self-injective Nakayama algebras using Hochschild homology methods.

Findings

Explicit quiver descriptions for Hochschild extension algebras

Connection between Hochschild homology and quiver structure

Method applicable to self-injective Nakayama algebras

Abstract

Let $T$ be a Hochschild extension algebra of a finite dimensional algebra $A$ over a field $K$ by the standard duality $A$-bimodule ${\rm Hom}_K(A,\,K)$. In this paper, we determine the ordinary quiver of $T$ if $A$ is a self-injective Nakayama algebra by means of the $\mathbb{N}$-graded second Hochschild homology group $HH_2(A)$ in the sense of Sk\"oldberg.