The Hochschild Cohomology Ring of Temperley–Lieb Algebras Revisited

2020 ◽  
Vol 27 (04) ◽  
pp. 669-686
Author(s):  
Weiguo Lyu ◽  
Yuling Wu
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Algebra Structure ◽  
Hochschild Cohomology Ring ◽  
Gerstenhaber Algebra

We determine the Gerstenhaber algebra structure on the Hochschild cohomology ring of Temperley–Lieb algebras in this paper.

scholarly journals Comparison morphisms and the Hochschild cohomology ring of truncated quiver algebras

2009 ◽  
Vol 322 (5) ◽  
pp. 1466-1497 ◽  
Author(s):  
Guillermo Ames ◽  
Leandro Cagliero ◽  
Paulo Tirao
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Hochschild Cohomology Ring

scholarly journals Hochschild cohomology ring of the modular group

2014 ◽  
Vol 26 (1) ◽  
pp. 1-25
Author(s):  
A. P. Alekhin ◽  
Yu. V. Volkov ◽  
A. I. Generalov
Keyword(s):  
Modular Group ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Hochschild Cohomology Ring

scholarly journals THE HOCHSCHILD COHOMOLOGY RING OF A CLASS OF SPECIAL BISERIAL ALGEBRAS

2010 ◽  
Vol 09 (01) ◽  
pp. 73-122 ◽  
Author(s):  
NICOLE SNASHALL ◽  
RACHEL TAILLEFER
Keyword(s):  
London Math ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Krull Dimension ◽  
Finitely Generated ◽  
Cohomology Rings ◽  
Hochschild Cohomology Ring ◽  
Special Biserial Algebras ◽  
Support Varieties

We consider a class of self-injective special biserial algebras ΛN over a field K and show that the Hochschild cohomology ring of dΛN is a finitely generated K-algebra. Moreover, the Hochschild cohomology ring of ΛN modulo nilpotence is a finitely generated commutative K-algebra of Krull dimension two. As a consequence the conjecture of [N. Snashall and Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc.88 (2004) 705–732], concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.

scholarly journals INVARIANCE OF THE GERSTENHABER ALGEBRA STRUCTURE ON TATE-HOCHSCHILD COHOMOLOGY

2019 ◽  
pp. 1-36
Author(s):  
Zhengfang Wang
Keyword(s):  
Hochschild Cohomology ◽  
Derived Category ◽  
Algebra Structure ◽  
Gerstenhaber Algebra ◽  
Morita Type

Keller proved in 1999 that the Gerstenhaber algebra structure on the Hochschild cohomology of an algebra is an invariant of the derived category. In this paper, we adapt his approach to show that the Gerstenhaber algebra structure on the Tate–Hochschild cohomology of an algebra is preserved under singular equivalences of Morita type with level, a notion introduced by the author in previous work.

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