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On Hochschild cohomology of a self-injective special biserial algebra obtained by a circular quiver with double arrows  [PDF]
Ayako Itaba
Mathematics , 2014,
Abstract: We calculate the dimensions of the Hochschild cohomology groups of a self-injective special biserial algebra $\Lambda_{s}$ obtained by a circular quiver with double arrows. Moreover, we give a presentation of the Hochschild cohomology ring modulo nilpotence of $\Lambda_{s}$ by generators and relations. This result shows that the Hochschild cohomology ring modulo nilpotence of $\Lambda_{s}$ is finitely generated as an algebra.
Hochschild cohomology for a class of some self-injective special biserial algebras of rank four  [PDF]
Takahiko Furuya
Mathematics , 2014,
Abstract: In this paper, we construct an explicit minimal projective bimodule resolution of a self-injective special biserial algebra $A_{T}$ ($T\geq0$) whose Grothendieck group is of rank $4$. As a main result, we determine the dimension of the Hochschild cohomology group ${\rm HH}^{i}(A_{T})$ of $A_{T}$ for $i\geq0$, completely. Moreover we give a presentation of the Hochschild cohomology ring modulo nilpotence ${\rm HH}^{*}(A_{T})/\mathcal{N}_{A_{T}}$ of $A_{T}$ by generators and relations in the case where $T=0$.
Vanishing of the Hochschild cohomology for some self-injective special biserial algebra of rank four  [PDF]
Takahiko Furuya,Takao Hayami
Mathematics , 2014,
Abstract: In this paper, we determine the dimensions of the Hochschild cohomology groups of some self-injective special biserial algebra whose Grothendieck group is of rank $4$. This result provides us with a negative answer to Happel's question in [H].
Hochschild cohomology of socle deformations of a class of Koszul self-injective algebras  [PDF]
Nicole Snashall,Rachel Taillefer
Mathematics , 2009,
Abstract: We consider the socle deformations arising from formal deformations of a class of Koszul self-injective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence is a finitely generated commutative algebra of Krull dimension 2.
Hochschild cohomology ring for self-injective algebras of tree class $E_6$  [PDF]
Mariya Pustovykh
Mathematics , 2013,
Abstract: We describe the Hochschild cohomology ring for one of the two self-injective algebras of tree class $E_6$ in terms of generators and relations.
The Hochschild Cohomology ring of preprojective algebras of type Ln  [PDF]
Estefanía Andreu Juan
Mathematics , 2010,
Abstract: We compute the Hochschild Cohomology of a finite-dimensional preprojective algebra of generalized Dynkin type Ln over a field of characteristic different from 2 . In particular, we describe the ring structure of the Hochschild Cohomology ring under the Yoneda product by giving an explicit presentation by generators and relations.
Hochschild cohomology of smash products and rank one Hopf algebras  [PDF]
S. M. Burciu,S. J. Witherspoon
Mathematics , 2006,
Abstract: We give some general results on the ring structure of Hochschild cohomology of smash products of algebras with Hopf algebras. We compute this ring structure explicitly for a large class of finite dimensional Hopf algebras of rank one.
Hochschild cohomology and support varieties for tame Hecke algebras  [PDF]
Sibylle Schroll,Nicole Snashall
Mathematics , 2009,
Abstract: We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras. As a consequence we obtain the result that the Hochschild cohomology ring modulo nilpotence of a Hecke algebra has Krull dimension 1 if the algebra is of finite type and has Krull dimension 2 if the algebra is of tame type.
Support varieties and the Hochschild cohomology ring modulo nilpotence  [PDF]
Nicole Snashall
Mathematics , 2008,
Abstract: This is a survey paper based on my talks at the 41st Symposium on Ring Theory and Representation Theory, held in Shizuoka University, Japan in September 2008, and will appear in the conference proceedings. The paper begins with a brief introduction to the use of Hochschild cohomology in developing the theory of support varieties for a module over an artin algebra, by Snashall and Solberg (Proc. London Math. Soc.(3) 88 (2004), 705-732). The paper then describes the current status of research concerning the structure of the Hochschild cohomology ring modulo nilpotence.
Gerstenhaber brackets on Hochschild cohomology of twisted tensor products  [PDF]
Lauren Grimley,Van C. Nguyen,Sarah Witherspoon
Mathematics , 2015,
Abstract: We construct the Gerstenhaber bracket on Hochschild cohomology of a twisted tensor product of algebras, and, as examples, compute Gerstenhaber brackets for some quantum complete intersections arising in work of Buchweitz, Green, Madsen, and Solberg. We prove that a subalgebra of the Hochschild cohomology ring of a twisted tensor product, on which the twisting is trivial, is isomorphic, as Gerstenhaber algebras, to the tensor product of the respective subalgebras of the Hochschild cohomology rings of the factors.
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