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Hochschild Cohomology of q-Schur Algebras

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Mayu Tsukamoto

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  1. Mayu Tsukamoto
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Correspondence to Mayu Tsukamoto.

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Presented by Henning Krause.

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Tsukamoto, M. Hochschild Cohomology of q-Schur Algebras. Algebr Represent Theor 20, 531–546 (2017). https://doi.org/10.1007/s10468-016-9653-0

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  • DOI: https://doi.org/10.1007/s10468-016-9653-0

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