Hochschild cohomology of algebras of semidihedral type. II. Local algebras

In terms of generators and relations, the Hochschild cohomology algebra is described for a family of local algebras of semidihedral type over the ground field that has characteristic not equal to 2. In relevant calculations, the free bimodule resolution that was constructed in another author’s paper is used. Bibliography: 22 titles.     

Hochschild cohomology for algebras of dihedral type,III: Local algebras in characteristic 2

The Hochschild cohomology algebra for a family of local algebras of dihedral type over a field of characteristic 2 is described in terms of generators and relations. Calculations use a free bimo-dule resolution constructed by the author elsewhere.     

Hochschild cohomology of Frobenius algebras

Let be a field, a finite-dimensional Frobenius -algebra and , the Nakayama automorphism of with respect to a Frobenius homomorphism . Assume that has finite order and that has a primitive -th root of unity . Consider the decomposition of , obtained by defining , and the decomposition of the Hochschild cohomology of , obtained from the decomposition of . In this paper we prove that and that if the decomposition of is strongly -graded, then acts on and .

     

Hochschild cohomology via incidence algebras

Given an algebra A, we associate an incidence algebra A() andcompare their Hochschild cohomology groups.     

Hochschild cohomology of truncated quiver algebras

For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles.     

Hochschild cohomology and graded Hecke algebras

We develop and collect techniques for determining Hochschild cohomology of skew group algebras and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of and, in particular, about graded Hecke algebras. We expand the definition of a graded Hecke algebra to allow a nonfaithful action of on , and we show that there exist nontrivial graded Hecke algebras for , in contrast to the case of the natural reflection representation. We prove that one of these graded Hecke algebras is equivalent to an algebra that has appeared before in a different form.

     

Hochschild cohomology of special biserial algebras

Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.     

Koszul代数的Hochschild上同调环

基于Buchweitz等人对Koszul代数的Hochschild上同调环的乘法结构的细致分析,给出了Koszul代数的Hochschild上同调环的乘法本质上是平行路的毗连的一个充要条件,并由此重新证明了二次三角string代数的Hochschild上同调环的乘法是平凡的,从而改进了Bustamante的证明.     

Hochschild cohomology of brauer tree algebras

The aim of this paper is to study the structure of the Hochschild cohomology ring of Brauer tree algebras. We explicitly describe the even cohomology ring by generators and relations. This generalizes results of [11] on the Hochschild cohomology of blocks of modular group algebras with cyclic defect groups.     

Hochschild cohomology of Möbius algebras

The additive structure of the Hochschild cohomology ring for a Möbius algebra is described. We use the structure of the bimodule minimal projective resolution of the algebra, constructed in a previous paper. Bibliography: 4 titles.     

On Hochschild cohomology rings of Fibonacci algebras

Let Λ be a Fibonacci algebra over a field k. The multiplication of Hochschild cohomology ring of Λ induced by the Yoneda product is described explicitly. As a consequence, the multiplicative structure of Hochschild cohomology ring of Λ is proved to be trivial.     

Hochschild cohomology and quantum Drinfeld Hecke algebras

Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit connection to Hochschild cohomology. We compute the relevant part of Hochschild cohomology for actions of many reflection groups, and we exploit computations from Naidu et al. (Proc Am Math Soc 139:1553–1567, 2011) for diagonal actions. By combining our work with recent results of Levandovskyy and Shepler (Can J Math 66:874–901, 2014) we produce examples of quantum Drinfeld Hecke algebras. These algebras generalize the braided Cherednik algebras of Bazlov and Berenstein (Selecta Math 14(3–4):325–372, 2009).     

Hochschild cohomology for periodic algebras of polynomial growth

We describe the dimensions of low Hochschild cohomology spaces of exceptional periodic representation-infinite algebras of polynomial growth. As an application we obtain that an indecomposable non-standard periodic representation-infinite algebra of polynomial growth is not derived equivalent to a standard self-injective algebra.     

On the Hochschild cohomology of tame Hecke algebras

We explicitly calculate a projective bimodule resolution for a special biserial algebra giving rise to the Hecke algebra H_q(S₄){{\mathcal H}_q(S_4)} when q = −1. We then determine the dimensions of the Hochschild cohomology groups.     

Self-injective algebras and the second Hochschild cohomology group

In this paper we study the second Hochschild cohomology group ${\mathrm{HH}}^2(\Lambda )$ of a finite dimensional algebra Λ. In particular, we determine ${\mathrm{HH}}^2(\Lambda )$ where Λ is a finite dimensional self-injective algebra of finite representation type over an algebraically closed field K and show that this group is zero for most such Λ; we give a basis for ${\mathrm{HH}}^2(\Lambda )$ in the few cases where it is not zero.     

Some results on the Hochschild cohomology of group algebras

In this paper we investigate structure of the second cohomology of a discrete group . First, for a -set we show that an isomorphism of vector spaces from onto exists, where is the set of orbits of . Next we define the notion of pseudoderivation and apply it for the calculation of .