The homology of algebras of pseudo-differential symbols and the noncommutative residue
type: Item
instance of: scholarly article
title: The homology of algebras of pseudo-differential symbols and the noncommutative residue
zbMATH Open document ID: 0646.58026
DOI: 10.1007/BF00539624
author: E. Getzler
author: Jean-Luc Brylinski
published in: \(K\)-Theory
publication date: 1987-01-01T00:00:00Z
review text: The Hochschild and cyclic homology groups of the algebra of pseudo- differential symbols \(\Psi^{\infty}(M)/\Psi^{-\infty}(M)\) on a smooth m-dimensional manifold M are calculated; the main result is that \(HH_*(\Psi^{\infty}(M)/\Psi^{-\infty}(M))=H^{2n-*}(S\quad *M\times {\mathbb{S}}^ 1,{\mathbb{C}}),\) \(HC_*(\Psi^{\infty}(M)/\Psi^{- \infty}(M))=H^{2n-*}(S^*M\times {\mathbb{S}}^ 1,{\mathbb{C}})[u].\)
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 14C35
zbMATH DE Number: 4054656
zbMATH Keywords: microlocal analysis
zbMATH Keywords: Hochschild and cyclic homologies
zbMATH Keywords: pseudo- differential operator
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00539624
OpenAlex ID: W2011038505
description: scientific article; zbMATH DE number 4054656