An example of a braided category of C*- algebras

Abstract

A braided category of C*-algebras is constructed. Its objects are C*-algebras endowed with an action of the group R, its morphisms are C*-algebras morphisms intertwining the action of R, the crossed product of its two objects essentially depends on the action of R on considered C*-algebras. Crossed products of any object with the algebra of all continuous vanishing at infinity functions on R and algebras of all continuous functions on one- and twodimensional tori are discussed.