C-*-Algebraic covariant structures

Abstract

We introduce covariant structures {(A, kappa), (a, alpha), ((a) over tilde, (alpha) over tilde)} formed of a separable C*-algebra A, a measurable twisted action (a, alpha) of the second-countable locally compact group G, a measurable twisted action ((a) over tilde, (alpha) over tilde) of another second-countable locally compact group ($) over tilde and a strictly continuous function kappa : G x (G) over tilde -> UM(A) suitably connected with (a, alpha) and ((a) over tilde, (alpha) over tilde). Natural notions of covariant morphisms and representations are considered, leading to a sort of twisted crossed product construction. Various C*-algebras emerge by a procedure that can be iterated indefinitely and that also yields new pairs of twisted actions. Some of these C*-algebras are shown to be isomorphic. The constructions are non-commutative, but are motivated by Abelian Takai duality that they eventually generalize.