English
Related papers

Related papers: Hochschild cohomology in toposes

200 papers

In this note we give a generalization for the higher order Hochschild cohomology and show that the secondary Hochschild cohomology is a particular case of this new construction.

Rings and Algebras · Mathematics 2016-07-26 Bruce R. Corrigan-Salter , Mihai D. Staic

We study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of $C_\infty$-algebras thus generalising previous work…

Quantum Algebra · Mathematics 2007-05-23 Alastair Hamilton , Andrey Lazarev

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

We show that the continuous Hochschild cohomology and the differential Hochschild cohomology of the Hida test algebra endowed with the normalized Wick product are the same.

Quantum Algebra · Mathematics 2008-09-30 Rémi Léandre

To a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on…

Algebraic Geometry · Mathematics 2022-03-24 Elisa Hartmann

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 dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the…

Group Theory · Mathematics 2022-04-22 David Benson , Radha Kessar , Markus Linckelmann

We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone…

Differential Geometry · Mathematics 2013-10-11 Christian Becker

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…

Algebraic Topology · Mathematics 2025-04-21 Truong Hoang

Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude…

Rings and Algebras · Mathematics 2008-01-11 Anders J. Frankild , Peter Jorgensen

We describe the Hochschild cohomology ring for one of the two self-injective algebras of tree class $E_6$ in terms of generators and relations.

K-Theory and Homology · Mathematics 2013-11-21 Mariya Pustovykh

We discuss spectral sequences coming from Whitehead filtrations in the computation of topological Hochschild homology of ring spectra. Using cyclic invariance, this makes for simple computations of $THH$ of connective rings $R$ with…

Algebraic Topology · Mathematics 2025-07-23 Logan Hyslop

This sketch argues that work of Hesselholt on the topological Hochschild homology of $\Cp$ extends, using work of Scholze and others, to define complex orientations for a version of topological Hochschild homology for rings of integers in a…

Algebraic Topology · Mathematics 2020-03-06 Jack Morava

We consider L-infinity quasi-isomorphisms for Hochschild cochains whose structure maps admit "graphical expansion". We introduce the notion of stable formality quasi-isomorphism which formalizes such an L-infinity quasi-isomorphism. We…

K-Theory and Homology · Mathematics 2019-12-13 Vasily Dolgushev

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…

Representation Theory · Mathematics 2016-06-07 Lauren Grimley

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category…

Category Theory · Mathematics 2014-04-16 Alin Stancu

We extend the notion of monogenic extension to the noncommutative setting, and we study the Hochschild cohomology ring of such an extension. As an aplication we complete the computation of the cohomology ring of the rank one Hopf algebras…

K-Theory and Homology · Mathematics 2007-06-13 Marco Farinati , Jorge A. Guccione , Juan J. Guccione

A certain Grothendieck topology assigned to a metric space gives rise to a sheaf cohomology theory which sees the coarse structure of the space. Already constant coefficients produce interesting cohomology groups. In degree 0 they see the…

Algebraic Topology · Mathematics 2022-05-04 Elisa Hartmann

Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…

Differential Geometry · Mathematics 2020-12-03 Lukas Miaskiwskyi

We study higher Hochschild homology evaluated on wedges of circles, viewed as a functor on the category of free groups. The main results use coefficients arising from square-zero extensions; this is motivated by work of Turchin and…

Algebraic Topology · Mathematics 2024-12-12 Geoffrey Powell , Christine Vespa