Some algebraic properties of cyclic homology groups
type: Item
instance of: scholarly article
title: Some algebraic properties of cyclic homology groups
zbMATH Open document ID: 0636.18005
DOI: 10.1007/BF00539623
author: Christine E. Hood
author: John D. S. Jones
published in: \(K\)-Theory
publication date: 1987-01-01T00:00:00Z
review text: By its periodicity the cyclic cohomology HC *(A) of an associative algebra A over a commutative ring K becomes a module over the polynomial ring K[X] [\textit{J. D. S. Jones}: Cyclic homology and equivariant homology, Invent. Math. 87, 403-424 (1987)]. \(HC\) \(-_*(A)\) denotes the homology theory dual over K[X] which is different from the K[X]-module \(HC_*(A)\). Both HC *(A) and \(HC_*(A)\) are expressed in terms of \(HC\) \(-_*(A)\). Then, K[X] bilinear products and coproducts are constructed and systematically studied. Finally, the authors prove various Künneth theorems and gain a product preserving Chern character \(K_*(A)\to HC\) \(-_*(A)\), where \(K_*(A)\) is the algebraic K-theory of A.
Mathematics Subject Classification ID: 18G35
zbMATH DE Number: 4036042
zbMATH Keywords: cyclic homology
zbMATH Keywords: products in homology
zbMATH Keywords: cyclic cohomology
zbMATH Keywords: Künneth theorems
zbMATH Keywords: Chern character
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00539623
OpenAlex ID: W2015556085
description: scientific article; zbMATH DE number 4036042