Rotation numbers for automorphisms of C^∗ algebras

Ruy Exel

Vol. 127 (1987), No. 1, 31–89

DOI: 10.2140/pjm.1987.127.31

Abstract

Poincaré’s notion of rotation number for a homeomorphism of the circle is generalized to a large class of automorphisms of C^∗ algebras. This is accomplished by the introduction of a C^∗ algebraic notion of determinant. A formula is obtained for the range of a trace on the K₀ group of a cross product by Z in terms of the rotation number of the automorphism involved.

Mathematical Subject Classification 2000

Primary: 46L40

Secondary: 58F11

Milestones

Received: 14 October 1985

Revised: 21 March 1986

Published: 1 March 1987