Fibrewise stratification of group representations

Benson, David John; Iyengar, Srikanth B.; Krause, Henning; Pevtsova, Julia

doi:10.5802/art.6

Benson, David John ¹ ; Iyengar, Srikanth B.² ; Krause, Henning ³; Pevtsova, Julia ⁴

¹ Institute of Mathematics, University of Aberdeen, King’s College, Aberdeen AB24 3UE, Scotland U.K.
² Department of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.
³ Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany.
⁴ Department of Mathematics, University of Washington, Seattle, WA 98195, U.S.A.

Annals of Representation Theory, Volume 1 (2024) no. 1, pp. 97-124.

Abstract

Given a finite cocommutative Hopf algebra $A$ over a commutative regular ring $R$ , the lattice of localising tensor ideals of the stable category of Gorenstein projective $A$ -modules is described in terms of the corresponding lattices for the fibres of $A$ over the spectrum of $R$ . Under certain natural conditions on the cohomology of $A$ over $R$ , this yields a stratification of the stable category. These results apply when $A$ is the group algebra over $R$ of a finite group, and also when $A$ is the exterior algebra on a finite free $R$ -module.

Received: 2023-01-05
Revised: 2023-08-27
Accepted: 2023-12-30
Published online: 2024-05-23

DOI: 10.5802/art.6

Classification: 16G30, 18G80, 20C10, 20J06
Mots-clés : Cocommutative Hopf algebra, group algebra, integral representation, stratification, stable module category

Author's affiliations:

Benson, David John ¹; Iyengar, Srikanth B. ²; Krause, Henning ³; Pevtsova, Julia ⁴

¹ Institute of Mathematics, University of Aberdeen, King’s College, Aberdeen AB24 3UE, Scotland U.K.
² Department of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.
³ Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany.
⁴ Department of Mathematics, University of Washington, Seattle, WA 98195, U.S.A.

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Benson, David John; Iyengar, Srikanth B.; Krause, Henning; Pevtsova, Julia. Fibrewise stratification of group representations. Annals of Representation Theory, Volume 1 (2024) no. 1, pp. 97-124. doi : 10.5802/art.6. https://art.centre-mersenne.org/articles/10.5802/art.6/

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