The stable category and invertible modules for infinite groups

We construct a well-behaved stable category of modules for a large class of infinite groups. We then consider its Picard group, which is the group of invertible (or endotrivial) modules. We show how this group can be calculated when the group acts on a tree with finite stabilisers.

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Published in:Advances in mathematics (New York. 1965) 2019-12, Vol.358, p.106853, Article 106853
Main Authors: Mazza, Nadia, Symonds, Peter
Format: Article
Language:English
Subjects:
Endotrivial module
Invertible module
Stable category
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description We construct a well-behaved stable category of modules for a large class of infinite groups. We then consider its Picard group, which is the group of invertible (or endotrivial) modules. We show how this group can be calculated when the group acts on a tree with finite stabilisers.
doi_str_mv 10.1016/j.aim.2019.106853
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subjects Endotrivial module
Invertible module
Stable category
title The stable category and invertible modules for infinite groups
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