The stable category and invertible modules for infinite groups

2019/02/18 by Mazza, Nadia, Symonds, Peter · 2 citations
#20C07 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1902.06533

Abstract

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.

Cited by

• The proper stable module category of a group algebra
• Monoidal model structures over infinite groups

Related

• On the Picard group of the stable module category for infinite groups
• Some finiteness results in the category U
• Decompositions of the stable module ∞-category
• Some relative stable categories are compactly generated
• (Co)stratification of stable categories for infinite groups