Applications of the Connes Spectrum to C1-dynamical systems,III |
| |
Authors: | Dorte Olesen Gert K Pedersen |
| |
Institution: | Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Denmark |
| |
Abstract: | For a C1-dynamical system (A, G, α) we show that the crossed product C1-algebra is induced from a simple C1-algebra equipped with an action of the Connes Spectrum, provided that A is G-simple and all isotropy subgroups of G under the action on the primitive ideal space of A are discrete. We then study the Borchers Spectrum of α and characterize its annihilator in G as the group of locally derivable automorphisms, under the assumption that the Arveson Spectrum of α is compact modulo the Borchers Spectrum. Finally a properly outer automorphism α is characterized by a series of equivalent conditions, one of which says that α is not close to the inner automorphisms on any ideal, another that α is not universally weakly inner on any ideal, and a third that the Borchers Spectrum of α on any invariant hereditary C1-subalgebra is non-zero. This characterization leads to the conclusion that α is aperiodic (i.e., every non-zero power is properly outer) precisely when the Connes Spectrum of α is the full circle group. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|