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Simplicite des Groupes Unitaires Definis par un Facteur Simple

Published online by Cambridge University Press:  20 November 2018

Thierry Giordano  and
Pierre De La Harpe
Thierry Giordano
Affiliation:
Institut de Mathématiques UniversitéDe Neuchâtel , CH-2000 Neuchâtel
Pierre De La Harpe
Affiliation:
Institut de Mathématiques UniversitéDe Neuchâtel , CH-2000 Neuchâtel
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Abstract

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Let B be a σ-finite von Neumann factor of type II1 or III and let σ be an involutory *-antiautomorphism of B. We consider U(B) the unitary group of B and its subgroup G = {g ∈U(B) | σ(g) = g*}, which are unitary classical groups. In this paper, we prove that G has a unique non trivial normal subgroup, which is its centre {±1}.

Keywords

46410
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 87 - 95
Copyright
Copyright © Canadian Mathematical Society 1984

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