Higher polyhedral K-groups

Autor(en): Bruns, W 
Gubeladze, J
Stichwörter: Mathematics; Mathematics, Applied; RING
Erscheinungsdatum: 2003
Herausgeber: ELSEVIER SCIENCE BV
Journal: JOURNAL OF PURE AND APPLIED ALGEBRA
Volumen: 184
Ausgabe: 2-3
Startseite: 175
Seitenende: 228
Zusammenfassung: 
We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin's theory and Quillen's construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by polyhedral geometry. This paper is a continuation of Bruns and Gubeladze (Polyhedral K-2, Manuscr. Math.) which is devoted to the study of polyhedral aspects of the classical Steinberg relations. The present work explores the polyhedral geometry behind Suslin's well known proof of the coincidence of the classical Volodin's and Quillen's theories. We also determine all K-groups coming from two-dimensional polytopes. (C) 2003 Elsevier B.V. All rights reserved.
ISSN: 00224049
DOI: 10.1016/S0022-4049(03)00037-9

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