Gluing representations via idempotent modules and constructing endotrivial modules

Paul Balmer, David J. Benson, Jon F. Carlson

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let G be a finite group and k be a field of characteristic p. We show how to glue Rickard idempotent modules for a pair of open subsets of the cohomology variety along an automorphism for their intersection. The result is an endotrivial module. An interesting aspect of the construction is that we end up constructing finite dimensional endotrivial modules using infinite dimensional Rickard idempotent modules. We prove that this construction produces a subgroup of finite index in the group of endotrivial modules. More generally, we also show how to glue any pair of kG-modules. (C) 2008 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)173-193
Number of pages21
JournalJournal of Pure and Applied Algebra
Volume213
Issue number2
Early online date15 Jul 2008
DOIs
Publication statusPublished - Feb 2009

Keywords

  • infinitely generated modules
  • equivariant cohomolgy ring
  • endo-permutation modules
  • spectrum
  • complexity
  • varieties

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