Hochschild Cohomology of q-Schur Algebras

We compute the Hochschild cohomology of any block of q -Schur algebras. We focus on the even part of this Hochschild cohomology ring. To compute the Hochschild cohomology of q -Schur algebras, we prove the following two results: first, we construct two graded algebra surjections between the Hochschi...

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Bibliographic Details
Published inAlgebras and representation theory Vol. 20; no. 3; pp. 531 - 546
Main Author Tsukamoto, Mayu
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2017
Springer Nature B.V
Subjects
Algebra
Associative Rings and Algebras
Commutative Rings and Algebras
Isomorphism
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
16E40
Hochschild cohomology
Schur algebras
Quasi-hereditary algebras
20G43
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Summary:We compute the Hochschild cohomology of any block of q -Schur algebras. We focus on the even part of this Hochschild cohomology ring. To compute the Hochschild cohomology of q -Schur algebras, we prove the following two results: first, we construct two graded algebra surjections between the Hochschild cohomologies of quasi-hereditary algebras because all q -Schur algebras over a field are quasi-hereditary. Second, we give the graded algebra isomorphism of Hochschild cohomologies by using a certain derive equivalence.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-016-9653-0