2024-02-25T11:21:54Z
https://soar-ir.repo.nii.ac.jp/oai
oai:soar-ir.repo.nii.ac.jp:00015853
2022-12-14T04:01:45Z
1544:1545
Cohomology Algebras of Blocks of Finite Groups and Brauer Correspondence II
Sasaki, Hiroki
Finite group
Block
Source modules
Brauer correspondence
Green correspondence
Hochschild cohomology
Block cohomology
Block variety
Let k be an algebraically closed field of characteristic p. We shall discuss the cohomology algebras of a block ideal B of the group algebra kG of a finite group G and a block ideal C of the block ideal of kH of a subgroup H of G which are in Brauer correspondence and have a common defect group, continuing (Kawai and Sasaki, Algebr Represent Theory 9(5):497-511, 2006). We shall define a (B,C)-bimodule L. The k-dual L (*) induces the transfer map between the Hochschild cohomology algebras of B and C, which restricts to the inclusion map of the cohomology algebras of B into that of C under some condition. Moreover the module L induces a kind of refinement of Green correspondence between indecomposable modules lying in the blocks B and C; the block varieties of modules lying in B and C which are in Green correspondence will also be discussed.
Article
ALGEBRAS AND REPRESENTATION THEORY. 13(4):445-465 (2010)
journal article
SPRINGER
2010-08
application/pdf
ALGEBRAS AND REPRESENTATION THEORY
4
13
445
465
1386-923X
AA11256919
https://soar-ir.repo.nii.ac.jp/record/15853/files/cohomology-BrauerII.pdf
eng
10.1007/s10468-009-9131-z
https://doi.org/10.1007/s10468-009-9131-z
The final publication is available at www.springerlink.com