English
Related papers

Related papers: Hochschild Cohomology Theories in White Noise Anal…

200 papers

We introduce a formalism of Hochschild (co)-homology for $\mathcal{D}$-cap modules on smooth rigid analytic spaces based on the homological tools of Ind-Banach $\mathcal{D}$-cap modules. We introduce several categories of $\mathcal{D}$-cap…

Number Theory · Mathematics 2026-02-10 Fernando Peña Vázquez

The stochastic parabolic equations with random potentials, driving forces and initial conditions are considered. The Wick product is used to give sense to the product of two generalized stochastic processes, and the existence and uniqueness…

Probability · Mathematics 2022-04-07 Snežana Gordić , Tijana Levajković , Ljubica Oparnica

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 show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby we obtain a number of positive characteristic stable invariants, such…

Representation Theory · Mathematics 2023-03-08 Benjamin Briggs , Lleonard Rubio y Degrassi

We define a topological Hochschild (THH) and cyclic (TC) homology theory for differential graded (dg) categories and construct several non-trivial natural transformations from algebraic K-theory to THH(-). In an intermediate step, we prove…

Algebraic Topology · Mathematics 2014-10-01 Goncalo Tabuada

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…

Rings and Algebras · Mathematics 2007-05-23 Yunge Xu , Yang Han , Wenfeng Jiang

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.

K-Theory and Homology · Mathematics 2007-08-30 Petter Andreas Bergh

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 show that the ordinary cohomology functor from the category of augmented $k$-algebras to itself exchanges coproducts and products, and that Hochschild cohomology is close to sending coproducts to products if the factors are…

Representation Theory · Mathematics 2010-07-26 Matthew Towers

We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology…

Algebraic Topology · Mathematics 2011-02-15 Katsuhiko Kuribayashi

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

Let A be a \C-algebra with an action of a finite group G, let $\natural$ be a 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$. We determine the Hochschild homology of $A \rtimes \C [G,\natural]$ for two…

Representation Theory · Mathematics 2023-09-12 Maarten Solleveld

The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristic homomorphism. We interpret it as an edge homomorphism in a…

Representation Theory · Mathematics 2017-06-19 Frank Neumann , Markus Szymik

We prove well-posedness and regularity for the stochastic pure Cahn-Hilliard equation under homogeneous Neumann boundary conditions, with both additive and multiplicative Wiener noise. In contrast with great part of the literature, the…

Analysis of PDEs · Mathematics 2018-10-03 Luca Scarpa

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…

K-Theory and Homology · Mathematics 2016-12-16 Bjørn Ian Dundas , Andrea Tenti

A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick's and Ito's theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and…

Operator Algebras · Mathematics 2008-06-24 Wilhelm von Waldenfels

We define the Hochschild and cyclic (co)homology groups for superadditive categories and show that these (co)homology groups are graded Morita invariants. We also show that the Hochschild and cyclic homology are compatible with the tensor…

Category Theory · Mathematics 2013-12-16 Deke Zhao

In this article we prove derived invariance of Hochschild-Mitchell homology and cohomology and we extend to $k$-linear categories a result by Barot and Lenzing concerning derived equivalences and one-point extensions. We also prove the…

K-Theory and Homology · Mathematics 2007-05-23 Estanislao Herscovich , Andrea Solotar

Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…

Rings and Algebras · Mathematics 2020-08-27 Apurba Das

We define, for a regular scheme $S$ and a given field of characteristic zero $\KK$, the notion of $\KK$-linear mixed Weil cohomology on smooth $S$-schemes by a simple set of properties, mainly: Nisnevich descent, homotopy invariance,…

Algebraic Geometry · Mathematics 2012-03-20 Denis-Charles Cisinski , Frédéric Déglise