Related papers: Hochschild Cohomological Dimension is Not Upper Se…
A concrete lower-bound for the Hochschild cohomological dimension of a commutative $k$-algebra, in terms of three other homological invariants is obtained. This result is then used to show that most $k$-algebras fail to be quasi-free, even…
Hochschild (co)homology and Pirashvili's higher order Hochschild (co)homology are useful tools for a variety of applications including deformations of algebras. When working with higher order Hochschild (co)homology, we can consider the…
In 1989 Happel conjectured that for a finite-dimensional algebra $A$ over an algebraically closed field $k$, $\gl A< \infty$ if and only if $\hch A < \infty$. Recently Buchweitz-Green-Madsen-Solberg gave a counterexample to Happel's…
For a truncated quiver algebra over a field of arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finite-dimensional if and only if its global dimension is…
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…
We show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semi-continuity of algebraic…
In 1989, D. Happel pointed out for a possible connection between the global dimension of a finite-dimensional algebra and its Hochschild cohomology: is it true that the vanishing of Hochschild cohomology higher groups is sufficient to…
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-associative algebra $A$ carries a Gerstenhaber structure. In…
Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule…
Higher Hochschild homology is the analog of the homology of spaces, where the context for the coefficients -- which usually is that of abelian groups -- is that of commutative algebras. Two spaces that are equivalent after a suspension have…
Let $B$ be a commutative algebra and $A$ be a $B$-algebra (determined by an algebra homomorphism $\varepsilon:B\rightarrow A$). M. D. Staic introduced a Hochschild like cohomology $H^{\bullet}((A,B,\varepsilon);A)$ called secondary…
An associative algebra is nothing but an odd quadratic codifferential on the tensor coalgebra of a vector space, and an A-infinity algebra is simply an arbitrary odd codifferential. Hochschild cohomology classifies the deformations of an…
It is established in this work that second Hochshild cohomology group of the associative conformal algebra Cend_{1,x} is zero. As a corollary, this algebra split off in each extension with a nilpotent kernel. Key words: associative…
Dieter Happel asked the following question: If the $n$-th Hochschild cohomology group of a finite dimensional algebra $\Gamma$ over a field vanishes for all sufficiently large $n$, is the global dimension of $\Gamma$ finite? We give a…
In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology…
In a previous paper, the author compute the dimension of Hochschild cohomology groups of Jacobian algebras from (unpunctured) triangulated surfaces, and gave a geometric interpretation of those numbers in terms of the number of internal…
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…
We prove that, for any Hausdorff continuum X, if dim X > 1 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then dim C(X) = 2 or C(X) is not a C-space. This generalizes results…
Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH*(kC) --> H*(|C|,k) and prove it is split surjective. This…
A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms…