Hermitian groups and \(K\)-theory
type: Item
instance of: scholarly article
title: Hermitian groups and \(K\)-theory
zbMATH Open document ID: 0899.19003
DOI: 10.1023/A:1007725531627
author: Guoping Tang
published in: \(K\)-Theory
publication date: 1998-10-28T00:00:00Z
review text: Let \(R\) be a ring with involution \(\bar{\phantom\lambda}\), and let \(\lambda\) be a central element from \(R\), such that \(\lambda \bar{\lambda} = 1\). The author studies the functors \(K_1\) and \(K_2\) of the category of non-singular \(\lambda\)-Hermitian spaces on finitely generated projective \(R\)-modules in the framework of the theory of \(\Lambda\)-quadratic modules developed by \textit{A. Bak} [cp. ``\(K\)-theory of forms'', Ann. Math. Stud. 98 (1981; Zbl 0465.10013)]. In particular, the elementary subgroup of the general Hermitian group and the Hermitian Steinberg group are defined, and it is shown that the Hermitian Whitehead lemma holds and that the Hermitian Steinberg group is the universal central extension of the elementary subgroup of the general Hermitian group in analogy with the linear and the quadratic case.
Mathematics Subject Classification ID: 19G38
Mathematics Subject Classification ID: 19B99
Mathematics Subject Classification ID: 19C99
zbMATH DE Number: 1139538
zbMATH Keywords: metabolic forms
zbMATH Keywords: general Hermitian group
zbMATH Keywords: Hermitian Steinberg group
reviewed by: Manfred Kolster
MaRDI profile type: Publication
full work available at URL: a:1007725531627
OpenAlex ID: W1981730041
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description: scientific article; zbMATH DE number 1139538