Work

Endotrivial modules for finite groups schemes II

Year: 2011

Type: preprint

Abstract: It is well known that if G is a finite group then the group of endotrivial modules is finitely generated. In this paper we prove that for an arbitrary finite group scheme G, and for any fixed integer n > 0, there are only finitely many isomorphism classes of endotrivial modules of dimension n. This provides evidence to support the speculation that the group of endotrivial modules for a finite group scheme is always finitely generated. The result also has some applications to questions about lifting and twisting the structure of endotrivial modules in the case that G is an infinitesimal group scheme associated to an algebraic group.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1104.0226

Authors: Carlson, Jon F., Nakano, Daniel K.

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Modular representations of finite groups, Cohomology, Geometry and Representation Theory: Algebraic Groups, Quantum Groups and Lie Superalgebras

OpenAlex ID: W1988674733

Cites: 19

Cited by: 2

Related to: 20