Finite group characters on free resolutions

TL;DR

This paper presents an algorithm to compute characters of finite groups acting on minimal free resolutions of modules over polynomial rings, enhancing understanding of their structure and invariants.

Contribution

It introduces a novel algorithm for explicitly computing group characters on free resolutions, linking group actions to algebraic invariants.

Findings

Algorithm efficiently computes group characters on free resolutions.

Provides explicit descriptions of group actions on differentials.

Facilitates new insights into Betti numbers and module structure.

Abstract

Under reasonable assumptions, a group action on a module extends to the minimal free resolutions of the module. Explicit descriptions of these actions can lead to a better understanding of free resolutions by providing, for example, convenient expressions for their differentials or alternative characterizations of their Betti numbers. This article introduces an algorithm for computing characters of finite groups acting on minimal free resolutions of finitely generated graded modules over polynomial rings.