On continuous and differential Hochschild cohomology
type: Item
instance of: scholarly article
title: On continuous and differential Hochschild cohomology
zbMATH Open document ID: 0939.16004
DOI: 10.1023/A:1007574526283
author: François Nadaud
published in: Letters in Mathematical Physics
publication date: 2000-05-02T00:00:00Z
review text: For \(A\), the algebra of smooth complex functions over a manifold \(M\), and \(V^*\) the space of skew multivector fields over \(M\), the author constructs canonical isomorphisms between Hochschild cohomology spaces \(H^*_{\text{cont}}(A,A)=H^*_{\text{diff}}(A,A)=V^*\). So, continuous and differential deformation theories of \(A\) coincide. The author, after some classical facts about Hochschild cohomology of commutative algebras, constructs the Koszul resolution of \(A\), embedded in the bar resolution, when \(M\) is an open subset \(U\) of \(\mathbb{R}^n\) and proves the topological part and the differential case of the main theorem. After developing the techniques of restriction and extension of cochains from one manifold to another the general case of the main result is proved.
reviewed by: Corina Mohorianu
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 13D10
Mathematics Subject Classification ID: 16S80
Mathematics Subject Classification ID: 55N35
zbMATH DE Number: 1275463
zbMATH Keywords: algebras of smooth complex functions
zbMATH Keywords: skew multivector fields
zbMATH Keywords: Hochschild cohomology spaces
zbMATH Keywords: differential deformation theories
zbMATH Keywords: Koszul resolutions
zbMATH Keywords: restrictions of cochains
zbMATH Keywords: extensions of cochains
MaRDI profile type: Publication
full work available at URL: a:1007574526283
OpenAlex ID: W137696708
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description: scientific article; zbMATH DE number 1275463