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Hochschild cohomology rings of tame Hecke algebras

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Abstract

Let A be a tame Hecke algebra of type A. Based on the minimal projective bimodule resolution \({(\mathbb{P} , \delta)}\) of A constructed by Schroll and Snashall, we first give an explicit description of the so-called “comultiplicative structure” of the generators of each term P n in \({(\mathbb{P} , \delta)}\) , and then apply it to define a chain map \({\Delta: \mathbb{P} \rightarrow \mathbb{P} \otimes_A \mathbb{P}}\) and thus show that the cup product in the level of cochains for the tame Hecke algebra A is essentially juxtaposition of parallel paths up to sign. As a consequence, we determine the structure of the Hochschild cohomology ring of A under the cup product by giving an explicit presentation by generators and relations.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Hubei University, Wuhan, 430062, P. R. China

    Yunge Xu & Tiwei Zhao

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  1. Yunge Xu
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  2. Tiwei Zhao
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Correspondence to Yunge Xu.

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Xu, Y., Zhao, T. Hochschild cohomology rings of tame Hecke algebras. manuscripta math. 142, 491–512 (2013). https://doi.org/10.1007/s00229-013-0613-2

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  • DOI: https://doi.org/10.1007/s00229-013-0613-2

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