Abstract
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.
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This work is supported by Grant-in-Aid for Scientific Research (C) (17540032), Japan Society for the Promotion of Science.
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Sasaki, H. Cohomology Algebras of Blocks of Finite Groups and Brauer Correspondence II. Algebr Represent Theor 13, 445–465 (2010). https://doi.org/10.1007/s10468-009-9131-z
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DOI: https://doi.org/10.1007/s10468-009-9131-z
Keywords
- Finite group
- Block
- Source modules
- Brauer correspondence
- Green correspondence
- Hochschild cohomology
- Block cohomology
- Block variety