2022-08-14T13:50:23Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000158532021-10-27T01:52:58Z1544:1545Cohomology Algebras of Blocks of Finite Groups and Brauer Correspondence IISasaki, HirokiThe final publication is available at www.springerlink.comFinite groupBlockSource modulesBrauer correspondenceGreen correspondenceHochschild cohomologyBlock cohomologyBlock varietyLet 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.ArticleALGEBRAS AND REPRESENTATION THEORY. 13(4):445-465 (2010)SPRINGER2010-08engjournal articleAMhttp://hdl.handle.net/10091/16145https://soar-ir.repo.nii.ac.jp/records/15853https://doi.org/10.1007/s10468-009-9131-z10.1007/s10468-009-9131-z1386-923XAA11256919ALGEBRAS AND REPRESENTATION THEORY134445465https://soar-ir.repo.nii.ac.jp/record/15853/files/cohomology-BrauerII.pdfapplication/pdf161.7 kB2015-09-28