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A new look at the Crossed-Product of a C*-Algebra by a Semigroup of Endomorphisms

Research paper by Ruy Exel

Indexed on: 14 Mar '06Published on: 14 Mar '06Published in: Mathematics - Operator Algebras



Abstract

Let G be a group and let P be a subsemigroup of G. 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 V_g on A for each g in G, obeying a partial group law, and such that (V_g,V_{g^{-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.