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Related papers: Explicit Hochschild Cocycles for Gentle Algebras

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In this paper we calculate the Hochschild cohomology of gentle $A_\infty$-algebras of arc collections on marked surfaces without boundary components. When the underlying arc collection has no loops or two-cycles, we show that the dgla…

Rings and Algebras · Mathematics 2025-01-08 Raf Bocklandt , Jasper van de Kreeke

Within the framework of deformation quantization, a first step towards the study of star-products is the calculation of Hochschild cohomology. The aim of this article is precisely to determine the Hochschild homology and cohomology in two…

Mathematical Physics · Physics 2008-09-17 Frédéric Butin

In this paper, we give an explicit description about the second Hochschild cohomology groups of bipartite Brauer graph algebras with trivial grading. Based on this, we provide geometric interpretations of deformations associated to some…

Rings and Algebras · Mathematics 2026-04-27 Yuming Liu , Zhengfang Wang , Bohan Xing

In this paper we calculate the Hochschild cohomology of graded skew-gentle algebras, together with its structure as graded commutative algebra under the cup product and its Lie algebra structure given by the Gerstenhaber bracket. One of the…

Representation Theory · Mathematics 2026-01-12 Xiuli Bian , Sibylle Schroll , Andrea Solotar , Xiao-chuang Wang , Can Wen

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…

Representation Theory · Mathematics 2016-10-12 Yadira Valdivieso-Díaz

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…

Commutative Algebra · Mathematics 2014-01-13 Ragnar-Olaf Buchweitz , Collin Roberts

We describe the (bigraded) Hochschild cohomology of graded gentle algebras along with the Gerstenhaber bracket and cup product. In particular, this yields a description of the Hochschild cohomology of partially wrapped Fukaya categories of…

Representation Theory · Mathematics 2026-01-12 Sebastian Opper

We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.

Rings and Algebras · Mathematics 2018-04-17 Goutam Mukherjee , Raj Bhawan Yadav

In this paper we define a new cohomology theory for a $B$-algebra $A$. We use this cohomology to study deformations of algebras $A[[t]]$, that have a $B$-algebra structure.

Rings and Algebras · Mathematics 2013-11-28 Mihai D. Staic

We compute Hochschild cohomology of projective hypersurfaces starting from the Gerstenhaber-Schack complex of the (restricted) structure sheaf. We are particularly interested in the second cohomology group and its relation with…

Algebraic Geometry · Mathematics 2016-02-15 Liyu Liu , Wendy Lowen

We compute the Hochschild cohomology of Hilbert schemes of points on surfaces and observe that it is, in general, not determined solely by the Hochschild cohomology of the surface, but by its "Hochschild-Serre cohomology": the bigraded…

Algebraic Geometry · Mathematics 2023-10-10 Pieter Belmans , Lie Fu , Andreas Krug

In this paper we determine the first Hochschild homology and cohomology with different coefficients for gentle algebras and we give a geometrical interpretation of these (co)homologies using the ribbon graph of a gentle algebra as defined…

Representation Theory · Mathematics 2020-02-12 Cristian Chaparro , Sibylle Schroll , Andrea Solotar

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…

Rings and Algebras · Mathematics 2017-12-04 Bruce R. Corrigan-Salter

A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…

funct-an · Mathematics 2008-02-03 S. C. Power

We examine the Hochschild cohomology for triangular algebras that capture some aspects of geometry and topology of the torus and of the quadric surface, and for deformations of these algebras. In particular, this shows that the cup product…

Rings and Algebras · Mathematics 2025-12-09 Vladimir Dotsenko , Andrea Solotar

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…

Representation Theory · Mathematics 2016-04-27 Mayu Tsukamoto

We give a formula for a cocycle generating the Hochschild cohomology of the Weyl algebra with coefficients in its dual.It is given by an integral over the configuration space of ordered points on a circle. Using this formula and a…

Quantum Algebra · Mathematics 2008-01-29 Boris Feigin , Giovanni Felder , Boris Shoikhet

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as…

Mathematical Physics · Physics 2017-09-07 Alexey A. Sharapov , Evgeny D. Skvortsov

We define the appropriate homological setting to study deformation theory of complete locally convex (curved) dg-algebras based on Positselski's contraderived categories. We define the corresponding Hochschild complex controlling…

Quantum Algebra · Mathematics 2025-12-25 Patrick Antweiler

We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer…

Rings and Algebras · Mathematics 2007-05-23 Anne V. Shepler , Sarah Witherspoon
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