Finite group characters on free resolutions. (November 2022)

• Record Type: Journal Article
• Authors: Galetto, Federico
• Is Part Of: Journal of symbolic computation. Volume 113(2022)
• Page Start: 29
• Page End: 38
• Publication Date: 2022-11
• Subjects: primary 13P20 -- secondary 13D02 13A50 20C15; Equivariant resolution -- Finite group -- Betti character -- Algorithm; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.02.001
• Languages: English
• ISSNs: 0747-7171

Abstract

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.