Smooth crossed product of minimal unique ergodic diffeomorphisms of a manifold and cyclic cohomology

摘要

Different diffeomorphisms can give the same C* crossed product algebra. Our main purpose is to show that we can still classify dynamical systems with some appropriate smooth crossed product algebras when their corresponding C* crossed product algebras are isomorphic. For this purpose, we construct two minimal unique ergodic diffeomorphisms alpha and beta of S-3 x S-6 x S-8. The C* algebras classification theory, smooth crossed product algebras considered by R. Nest and cyclic cohomology are used to show that alpha and beta give the same C* algebra and induce different smooth crossed product algebras.