Rotation numbers for automorphisms of C* algebras

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. © 1987 by Pacific Journal of Mathematics.