A note on the classification of UHF-algebras
type: Item
instance of: scholarly article
title: A note on the classification of UHF-algebras
zbMATH Open document ID: 0608.46048
DOI: 10.1007/BF01195812
author: B. George
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: Consider a real Hilbert bundle E with structure group contained in a real UHF algebra \({\mathcal A}\subset L(H)\). Then E may be orientable or not depending on the ''type'' of \({\mathcal A}\). More precisely, we proved the following result on the homotopical structure of the group G(\({\mathcal A})\) of invertible elements: G(\({\mathcal A})\) is connected iff \(K_ 0({\mathcal A})\) contains \({\mathbb{Z}}()\), the group of dyadic rationals. If this holds then G(\({\mathcal A})\) is even simply connected.
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 3983895
zbMATH Keywords: real Hilbert bundle
zbMATH Keywords: structure group
zbMATH Keywords: real UHF algebra
zbMATH Keywords: type
zbMATH Keywords: homotopical structure
zbMATH Keywords: group of dyadic rationals
MaRDI profile type: Publication
cites work: On the homotopical significance of the type of von Neumann algebra factors
cites work: On the classification of inductive limits of sequences of semisimple finite-dimensional algebras
cites work: K0 OF VON NEUMANN AND AF C* ALGEBRAS
cites work: Homotopy theory of infinite dimensional manifolds
cites work: Q3205815
cites work: On the homotopy type of the regular group of a real \(W^ *\)-algebra
description: scientific article; zbMATH DE number 3983895