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Hochschild cohomology rings of Temperley-Lieb algebras

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Abstract

The authors first construct an explicit minimal projective bimodule resolution (ℙ, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochschild cohomology ring of A based on a comultiplicative map Δ: ℙ → ℙ ⊗ A ℙ. As a consequence, the authors determine the multiplicative structure of Hochschild cohomology rings of both Temperley-Lieb algebras and representation-finite q-Schur algebras under the cup product by giving an explicit presentation by generators and relations.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Huanhuan Li, Yunge Xu & Yuan Chen

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Huanhuan Li

Authors
  1. Huanhuan Li
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  2. Yunge Xu
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  3. Yuan Chen
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Corresponding author

Correspondence to Yunge Xu.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11171325, 11371186, 11301161) and the Research Foundation of Education Bureau of Hubei Province of China (No. Q20131009).

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Li, H., Xu, Y. & Chen, Y. Hochschild cohomology rings of Temperley-Lieb algebras. Chin. Ann. Math. Ser. B 36, 613–624 (2015). https://doi.org/10.1007/s11401-015-0903-y

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  • DOI: https://doi.org/10.1007/s11401-015-0903-y

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