Abstract:
We deal with algebras of sphericl functions associated with
covariant systems over a compact group with locally compact group
action on 𝐶∗-algebras and compact subgroups and duality theory for
nonergodic actions. The quasi product actions of compact abelian
group on a 𝐶∗ - algebra and freeness of actions of finite abelian
groups on 𝐶∗-algebras and free of compact quantum groups on unital
𝐶∗ - algebras are considered. The Galois correspondence for compact
groups of automorphisms of von Neumann algebras with a
generalization to Kac algebras, for compact quantum group actions
and 𝐶∗-algebras are studied. The homoclinic groups and expansive
algebraic actions are presented. The invariant measures for
homeomorphisms with weak specification and orbit equivalence for
generalized Toeplitz subshifts are introduced. The generic points of
invariant measures for an amenable residually finite group actions
with the weak specification property for ergodic group
automorphisms of abelian groups are characterized.
