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 language | English |
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Pages (from-to) | 173-193 |
Number of pages | 21 |
Journal | Journal of Pure and Applied Algebra |
Volume | 213 |
Issue number | 2 |
Early online date | 15 Jul 2008 |
DOIs | |
Publication status | Published - Feb 2009 |
Keywords
- infinitely generated modules
- equivariant cohomolgy ring
- endo-permutation modules
- spectrum
- complexity
- varieties