Prestabilization for K1 of banach algebras

L. N. Vaserstein, B. A. Magurnt

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The injective stability for the general linear group modulo elementary matrices begins at one plus the stable range of the ring of entries. At one step earlier, the kernel of stabilization is perhaps larger than the group of elementary matrices. Using a Dieudonné-style determinant, it is shown that this kernel is generated by matrices of the form (1 + XY) (1 + XY), under certain conditions on the ring of entries, or in the relative case, on the ideal. For any ideal of stable rank one, the kernel is given in terms of generators (X + Z + XYZ) (X + Z + ZYX). Under somewhat stronger conditions, the kernel is shown to be a commutator subgroup.

Original languageEnglish (US)
Pages (from-to)69-96
Number of pages28
JournalLinear Algebra and Its Applications
Volume95
Issue numberC
DOIs
StatePublished - Oct 1987

Fingerprint

Banach algebra
Algebra
Elementary matrix
kernel
Electric commutators
Stable Rank
Ring
Commutator subgroup
General Linear Group
Stabilization
Injective
Modulo
Determinant
Generator
Range of data

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Cite this

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Prestabilization for K1 of banach algebras. / Vaserstein, L. N.; Magurnt, B. A.

In: Linear Algebra and Its Applications, Vol. 95, No. C, 10.1987, p. 69-96.

Research output: Contribution to journalArticle

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