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Setting the scene for Betti characters

Federico Galetto

Vol. 13 (2023), 45–51

Finite group actions on free resolutions and modules arise naturally in many interesting examples. Understanding these actions amounts to describing the terms of a free resolution or the graded components of a module as group representations which, in the nonmodular case, are completely determined by their characters. With this goal in mind, we introduce a Macaulay2 package for computing characters of finite groups on free resolutions and graded components of finitely generated graded modules over polynomial rings.

Macaulay2, equivariant resolution, finite group, Betti character
Mathematical Subject Classification
Primary: 13-04
Secondary: 13A50, 13D02, 13P20, 20C15
Supplementary material

BettiCharacters: a Macaulay2 package for computing finite group characters on free resolutions and graded modules.

Received: 30 June 2021
Revised: 26 February 2023
Accepted: 30 May 2023
Published: 28 August 2023
Federico Galetto
Department of Mathematics and Statistics
Cleveland State University
Cleveland, OH
United States