Uniqueness of products in higher algebraic K-theory
type: Item
instance of: scholarly article
title: Uniqueness of products in higher algebraic K-theory
zbMATH Open document ID: 0662.18009
author: Kazuhisa Shimakawa
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1988-01-01T00:00:00Z
review text: This paper presents an alternate way of studying the multiplicative structure of higher K-theory. For the most part, the author restricts his attention to K-theories E defined on permutative categories U on which the composition BU\(\to \Omega^{\infty}E_{\infty}U=\cup \Omega^ nE_ nU\) is a group completion. He defines a transformation to be multiplicative in terms of strong pairings (as opposed to the weak pairings in the sense of Whitehead). He then shows that the product structure on any such higher algebraic K-theory E is equivalent to those of May, Waldhausen, Shimada-Shimakawa and a modification of Loday's. Much of the work revolves around the notion of \(S_*\)-spectra showing that pairings of \(S_*\)-spectra determine pairings of the stable category.
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 4081801
zbMATH Keywords: product structure on higher algebraic K-theory
zbMATH Keywords: multiplicative structure of higher K-theory
zbMATH Keywords: permutative categories
zbMATH Keywords: strong pairings
zbMATH Keywords: spectra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195175327
OpenAlex ID: W2094224403
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DOI: 10.2977/PRIMS/1195175327
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description: scientific article; zbMATH DE number 4081801