Related papers: Hochschild cochains as a Frobenius algebra

We show that the Gerstenhaber-Schack cohomology of a Hopf algebra determines its Hochschild cohomology, and in particular its Gerstenhaber-Schack cohomological dimension bounds its Hochschild cohomological dimension, with equality of the…

In recent work, Hess and Shipley defined a theory of topological coHochschild homology (coTHH) for coalgebras. In this paper we develop computational tools to study this new theory. In particular, we prove a Hochschild-Kostant-Rosenberg…

In this paper, we study the Batalin-Vilkovisky structure on the Hochschild cohomology of quantum zigzag algebras $A_{q}$ of type $\widetilde{\mathbf{A}}_{1}$. We first calculate the dimensions of Hochschild homology groups and Hochschild…

Let $A=A(\alpha, \beta)$ be a graded down-up algebra with $({\rm deg}\,x, {\rm deg}\,y)=(1,n)$ and $\beta \neq 0$, and let $\nabla A$ be the Beilinson algebra of $A$. If $n=1$, then a description of the Hochschild cohomology group of…

Let $k$ be a noetherian commutative ring and let $G$ be a finite flat group scheme over $k$. Let $G$ act rationally on a finitely generated commutative $k$-algebra $A$. We show that the cohomology algebra $H^*(G,A)$ is a finitely generated…

We make use of the cotangent complex formalism developed by Lurie to formulate Quillen cohomology of algebras over an enriched operad. Additionally, we introduce a spectral Hochschild cohomology theory for enriched operads and algebras over…

The technique developed in Hochschild's works "Lie algebra kernels and cohomology " and "Cohomology classes of finite dimensional kernels for Lie algebras " [2],[3] can be applied to the special case of transitive Lie algebroids. Our task…

Let ${\rm N}_m(R) = \{ (a_{ij}) \in {\rm M}_m(R) \mid a_{11} = a_{22} = \cdots = a_{mm} \mbox{ and } a_{ij} = 0 \mbox{ for any } i > j \}$ for a commutative ring $R$. Then ${\rm N}_m(R)$ is a quadratic monomial algebra over $R$. We…

Let H be a differential graded Hopf algebra over a field k. This paper gives an explicit construction of a triple cochain complex that defines the Hochschild-Cartier cohomology of H. A certain truncation of this complex is the appropriate…

For a finite-dimensional Frobenius $k$-algebra $R$ with the Nakayama automorphism $\nu$ we define an algebra ${\rm HH}^*(R)^{\nu\uparrow}$. If the order of $\nu$ is not divisible by the characteristic of $k$, this algebra is isomorphic to…

We provide a factorization model for the continuous internal Hom, in the homotopy category of $k$-linear dg-categories, between dg-categories of equivariant factorizations. This motivates a notion, similar to that of Kuznetsov, which we…

We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level…

We develop a theory of internal Hochschild cohomology in a ringed topos. We construct it via the internal Hochschild cochain complex, as well as through derived functor/topos cohomology theory, and discuss its relationship to the absolute…

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…

In this paper, we compute the product structure of the Hochschild cohomology of preprojective algebras of quivers of type D and E over a field of characteristic zero.

For a finite dimensional monomial algebra $\Lambda$ over a field $K$ we show that the Hochschild cohomology ring of $\Lambda$ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated $K$-algebra of…

We prove that every open-closed homotopy algebra, introduced by Kajiura and Stasheff (arXiv: archive/0410291), naturally gives rise to an open-closed version of Hochschild cochain complex whose cohomology admits a canonical Gerstenhaber…

Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of…

We study string topology for classifying spaces of connected compact Lie groups, drawing connections with Hochschild cohomology and equivariant homotopy theory. First, for a compact Lie group $G$, we show that the string topology…

We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial,…