# Deleting or adding arrows of a bound quiver algebra and Hochschild (co)homology

## TL;DR

This paper investigates how the Hochschild (co)homology of bound quiver algebras varies with modifications to the quiver, such as adding or deleting arrows, using advanced homological tools.

## Contribution

It provides a detailed description of the changes in Hochschild (co)homology under quiver modifications employing relative Hochschild (co)homology and the Jacobi-Zariski sequence.

## Key findings

- Describes the impact of arrow modifications on Hochschild (co)homology.
- Utilizes the Jacobi-Zariski long exact sequence for analysis.
- Employs a one-step relative projective resolution of tensor algebras.

## Abstract

We describe how the Hochschild (co)homology of a bound quiver algebra changes when adding or deleting arrows to the quiver. The main tools are relative Hochschild (co)homology, the Jacobi-Zariski long exact sequence obtained by A. Kaygun and a one step relative projective resolution of a tensor algebra.