On Conditional Expectations Arising from Group Actions

Abstract

Induced conditional expectations of finite index on crossed product $C\ast$-algebras are considered which are non-algebraically of finite index. The characteristics of actions of (amenable) topological groups on compact Hausdorff spaces $X$ are investigated, ensuring the appearance of a well-defined induced conditional expectation on the corresponding commutative $C\ast$-a1gebra $C(X)$ and its property to be of finite index. For this purpose Hilbert $C\ast$-module and topological techniques are used. Special emphasis is placed on discrete group actions.