Topological full groups and structure of normalizers in transformation group C^∗-algebras

Jun Tomiyama

Vol. 173 (1996), No. 2, 571–583

DOI: 10.2140/pjm.1996.173.571

Abstract

Given a topological dynamical system Σ = (X,σ) for a homeomorphism σ on a compact space, we define the topological full group [Z_σ] with respect to the action σ. We then clarify the relations between normalizers in the transformation group C^∗-algebra A(Σ) and those homeomorphisms in the group [Z_σ]. The result implies the general isomorphism theorem between transformation group C^∗-algebras keeping their subalgebras of continuous functions.

Mathematical Subject Classification 2000

Primary: 46L55

Milestones

Received: 5 May 1993

Revised: 24 March 1994

Published: 1 April 1996