On some second Hochschild cohomology spaces for algebras of functions on a manifold
type: Item
instance of: scholarly article
title: On some second Hochschild cohomology spaces for algebras of functions on a manifold
zbMATH Open document ID: 0874.16008
DOI: 10.1023/A:1007330711440
author: Simone Gutt
published in: Letters in Mathematical Physics
publication date: 1997-09-30T00:00:00Z
review text: This paper deals with the second cohomology group for smooth functions on a manifold. Its main result relies very much on a construction by \textit{H. Omori, Y. Maeda} and \textit{A. Yoshioka} [in Contemp. Math. 179, 213-240 (1994; Zbl 0820.58027)]. It is shown that any continuous 2-cocycle can be written as \(C(u,v)=\delta F(u,v)+B(du,dv)\), where \(F\) is a continuous 1-cochain and \(B\) is a skewsymmetric contravariant 2-tensor on \(M\). The result remains true if ``continuous'' is replaced by a suitable condition of smoothness (goodness). Connected results have been obtained by \textit{G. Pinczon} [Lett. Math. Phys. 39, 143-156 (1997)].
reviewed by: Frédéric Patras
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 81S10
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B66
zbMATH DE Number: 989790
zbMATH Keywords: cohomology groups for smooth functions on manifolds
zbMATH Keywords: continuous 2-cocycles
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 989790