Shuffle products in higher \(K\)-theory
type: Item
instance of: scholarly article
title: Shuffle products in higher \(K\)-theory
zbMATH Open document ID: 0797.19003
DOI: 10.1016/0022-4049(94)90098-1
author: Bernhard Köck
published in: Journal of Pure and Applied Algebra
publication date: 1994-04-04T00:00:00Z
review text: Shuffle products appeared in the Eilenberg-MacLane homology theory of groups. The geometric origin is connected with a systematic simplicial decomposition of a product of simplices. The simplest case arises in the case of a simplicial decomposition of a \(d\)-dimensional torus. The \(\lambda\)-ring structure on the higher \(K\)-theory of a scheme \(X\) is the basic prerequisite to formulate and to prove Riemann-Roch type theorems in higher \(K\)-theory and to define motivic cohomology. The object of this paper is to study the \(\lambda\)-structure not only on the higher \(K\)- group \(K_ q(X)\), but already on the topological space (respectively on the simplicial set) whose homotopy groups are the higher \(K\)-groups. For recent related works, aside from those in the reference section, see, for example: \textit{F. Patras} [C. R. Acad. Sci., Paris, Sér. I 310, 501-504 (1990; Zbl 0695.55014); Bull. Soc. Math. Fr. 119, No. 2, 173-198 (1991; Zbl 0752.55014)], and \textit{R. Morelli} [The \(K\)-theory of a toric variety, Adv. Math. 100, No. 2, 154-182 (1993)].
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 19L10
zbMATH DE Number: 540917
zbMATH Keywords: shuffle products
zbMATH Keywords: simplicial decomposition
zbMATH Keywords: \(\lambda\)-ring
zbMATH Keywords: Riemann-Roch type theorems
zbMATH Keywords: higher \(K\)-theory
zbMATH Keywords: motivic cohomology
reviewed by: Chih-Han Sah
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90098-1
OpenAlex ID: W2004179816
cites work: Schur functors and Schur complexes
cites work: Q2546548
cites work: Q3701536
cites work: The loop space of the Q-construction
cites work: Exterior power operations on higher K-theory
cites work: Adams operations on higher \(K\)-theory
cites work: lambda-rings and algebraic K-theory
cites work: Das Adams-Riemann-Roch-Theorem in der höheren äquivarianten K-Theorie.
cites work: Q3720786
cites work: \(\lambda\)-structure en K-théorie algébrique
cites work: Higher algebraic K-theory: I
cites work: Q3826674
cites work: The cohomology of \(p\)-adic symmetric spaces
cites work: Opérations En K-Théorie Algébrique
cites work: Q3815404
cites work: Q4335131
description: scientific article; zbMATH DE number 540917