Related papers: (Co)homology of quantum complete intersections

The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…

We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric.

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be…

We determine the product structure on Hochschild cohomology of commutative algebras in low degrees, obtaining the answer in all degrees for complete intersection algebras. As applications, we consider cyclic extension algebras as well as…

We compute the Hochschild cohomology and homology of a class of quantum exterior algebras, with coefficients in twisted bimodules. As a result we obtain several interesting examples of the homological behavior of these algebras.

We determine the Hochschild cohomology algebras of the square-free monomial complete intersections. In particular, we provide a formula for the cup product which gives the cohomology module an algebra structure and then we describe this…

We explicitly calculate a projective bimodule resolution for a special biserial algebra giving rise to the Hecke algebra H_q(S_4) when q=-1. We then determine the dimensions of the Hochschild cohomology groups.

We compute the Hochschild cohomology ring of the algebras $A= k\langle X, Y\rangle/ (X^a, XY-qYX, Y^a)$ over a field $k$ where $a\geq 2$ and where $q\in k$ is a primitive $a$-th root of unity. We find the the dimension of $\mathrm{HH}^n(A)$…

The main objective of this paper is to provide a theory for computing the Hochschild cohomology of algebras arising from a linear category with finitely many objects and zero compositions. For this purpose, we consider such a category using…

We formulate the Gerstenhaber algebra structure of Hochschild cohomology of finite group extensions of some quantum complete intersections. When the group is trivial, this work characterizes the graded Lie brackets on Hochschild cohomology…

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…

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…

We compute the Hochschild cohomology of any block of $q$-Schur algebras. We focus the even part of this Hochschild cohomology ring. To compute the Hochschild cohomology of $q$-Schur algebras, we prove the following two results: first, we…

Let $A$ be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of $A$ with coefficients in the bimodule $A$ vanishes if and only if $A$ is representation finite and simply…

We compute the cohomology with trivial coefficients of Lie algebras $\mathfrak{m}_0$ and $\mathfrak{m}_2$ of maximal class over the field $\mathbb{Z}_2$. In the infinite-dimensional case, we show that the cohomology rings…

We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.

We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the…

We show that the Hochschild cohomology of a monomial algebra over a field of characteristic zero vanishes from degree two if the first Hochschild cohomology is semisimple as a Lie algebra. We also prove that first Hochschild cohomology of a…

We prove rigidity type results on the vanishing of stable (co)homology for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which…

We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.