Related papers: Hochschild homology and trivial extensions
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
The Hochschild cohomology rings for self-injective algebras of tree classes $E_7$ and $E_8$ with finite representation type was described in terms of generators and relations.
We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative.
We study the structure of certain classes of homologically trivial locally C*-algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a…
We show that for some finite group block algebras, with nontrivial defect groups, the first Hochschild cohomology is nontrivial. Along the way we obtain methods to investigate the nontriviality of the first Hochschild cohomology of some…
For an arbitrary finite-dimensional algebra $A$, we introduce a general approach to determining when its first Hochschild cohomology ${\rm HH}^1(A)$, considered as a Lie algebra, is solvable. If $A$ is moreover of tame or finite…
In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, we show that if the…
A theorem of Wiegerinck says that the Bergman space over any domain in $\mathbb C$ is either trivial or infinite dimensional. We generalize this theorem in the following form. Let E be a hermitian, holomorphic vector bundle over $\mathbb…
We construct a minimal projective bimodule resolution for every finite dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In…
The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded quasi-filiform algebra and the complemented space to the…
Let $\Gamma$ be a connected graph without loops, cycles or multiple edges and $Z(\Gamma)$ the corresponding zigzag algebra. Then every Jordan derivation of $Z(\Gamma)$ is a derivation. Moreover, we will prove that the dimension of 1th…
A consequence of the recent work of Ren and Zhu on Gorenstein projective dimensions of modules over Hopf algebras is that if $A$ and $B$ are Hopf algebras with bijective antipodes having equivalent linear tensor categories of comodules and…
We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology…
We prove that rational homology of the Torelli group of genus g is infinite dimensional, provided g>6. This means that rational homology of the Torelli space of genus g>6 is infinite dimensional. The Torelli groups with marked points are…
In this article we study extensions of Z_2-graded L_infinity algebras on a vector space of two even and one odd dimension. In particular, we determine all extensions of a super Lie algebra as an L_infinity algebra. Our convention on the…
We show that the homotopy category of injective $A$-modules is generically trivial if and only if the derived category of all modules is generically trivial for an algebra $A$. Moreover we show some connections between the generic objects,…
Let A be an Artin algebra and e an idempotent in A. It is an interesting topic to compare the homological dimension of the algebras A,A/AeA and eAe. For example, in [2], the relation among the global dimension of these algebras is discussed…
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
We prove that, over an algebraically closed field of characteristic zero, a semisimple Hopf algebra that has a nontrivial self-dual simple module must have even dimension. This generalizes a classical result of W. Burnside. As an…
The purpose of this note is to provide exposition for a proof of the statement in the title. This idea, that arbitrary cohomology classes (of high enough degree) of a finite group $G$ can be trivialized in a finite group extension, has been…