no. 1
Fibrewise stratification of group representations
Benson, David John1  ; Iyengar, Srikanth B.2 ; Krause, Henning3; Pevtsova, Julia4
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.

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:
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Accepted:
Published online:
DOI: 10.5802/art.6
Classification: 16G30, 18G80, 20C10, 20J06
Keywords: Cocommutative Hopf algebra, group algebra, integral representation, stratification, stable module category
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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