On the Exel Crossed Product of Topological Covering Maps |
| |
Authors: | Toke Meier Carlsen Sergei Silvestrov |
| |
Institution: | (1) Dipartimento di Matematica, University of Rome “La Sapienza”, P.le Aldo Moro, 2-00185 Roma, Italy |
| |
Abstract: | For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the
associated crossed product C
*-algebras C(X)⋊
α,ℒℕ introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological
freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In
this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering
map is topologically free; the canonical embedding of C(X) into C(X)⋊
α,ℒℕ is a maximal abelian C
*-subalgebra of C(X)⋊
α,ℒℕ; any nontrivial two sided ideal of C(X)⋊
α,ℒℕ has non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊
α,ℒℕ is faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product
C
*-algebras of homeomorphism dynamical systems. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|