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Compactly Generated Relative Stable Categories

Lookup NU author(s): Professor Peter Jorgensen

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Abstract

Let G be a finite group. The stable module category of G has been applied extensively in group representation theory. In particular, it has been used to great effect that it is a triangulated category which is compactly generated by the class of finitely generated modules. Let H be a subgroup of G. It is possible to define a stable module category of G relative to H. This is also a triangulated category, but no non-trivial examples have been known where it was compactly generated. While the finitely generated modules are compact objects, they do not necessarily generate the category. We show that the relative stable category is compactly generated if the group algebra of H has finite representation type. In characteristic p, this is equivalent to the Sylow p-subgroups of H being cyclic. © 2009 Springer Science+Business Media B.V.

Publication metadata

Author(s): Grime M, Jørgensen P

Publication type: Article

Publication status: Published

Journal: Algebras and Representation Theory

Year: 2011

Volume: 14

Issue: 2

Pages: 247-251

ISSN (print): 1386-923X

ISSN (electronic): 1572-9079

Publisher: Springer Netherlands

URL: http://dx.doi.org/10.1007/s10468-009-9187-9

DOI: 10.1007/s10468-009-9187-9

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