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| Hochschild Cohomology Rings of Temperley-Lieb Algebras |
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Citation： |
Huanhuan LI,Yunge XU,Yuan CHEN.Hochschild Cohomology Rings of Temperley-Lieb Algebras[J].Chinese Annals of Mathematics B,2015,36(4):613~624 |
| Page view： 1121
Net amount： 889 |
Authors： |
Huanhuan LI; Yunge XU; Yuan CHEN; |
Foundation： |
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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| Abstract： |
The authors first construct an explicit minimal projective bimodule resolution
$(\mathbb{P} ,\delta )$ 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 $\Delta:
\mathbb{P}\rightarrow\mathbb{P}\otimes_{A}\mathbb{P}$. 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. |
Keywords： |
Hochschild cohomology, Cup product, Temperley-Lieb algebra, q-Schur
algebra |
Classification： |
16E40, 16G10 |
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