Categories of Modules over Infinite Groups

Abstract

In the study of representation theory of groups, different kinds of triangulated categories arise naturally. We investigate some interesting generation properties of a range of derived categories associated to groups in Kropholler's hierarchy that need not be finite. Our investigations take us through dealing with many related cohomological properties of groups that are usually tackled with properties of various cohomological invariants. Connected to these invariants are some longstanding questions on the behaviour of certain classes of modules and certain families of groups that we also deal with. We also develop a theory around some generation operators in the standard module category that we use both to observe how generation properties travel from the module category to various derived categories and also to frame some of the other related questions that we mentioned earlier in terms of those generation operators.

Date of Award	31 Aug 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Peter Symonds (Supervisor) & Yuri Bazlov (Supervisor)