A new look at the crossed product of aC*-algebra by a semigroup of endomorphisms

Abstract

AbstractLet G be a group and let $P \subseteq G$ be a subsemigroup. In order to describe the crossed product of a C*-algebra A by an action of P by unital endomorphisms we find that we must extend the action to the whole group G. This extension fits into a broader notion of interaction groups which consists of an assignment of a positive operator Vg on A for each g in G, obeying a partial group law, and such that (Vg,Vg−1) is an interaction for every g, as defined in a previous paper by the author. We then develop a theory of crossed products by interaction groups and compare it to other endomorphism crossed product constructions.