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

Published online by Cambridge University Press:  01 June 2008

RUY EXEL
RUY EXEL*
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Brazil (email: [email protected])
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Abstract

Let G be a group and let 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 3 , June 2008 , pp. 749 - 789
Copyright
Copyright © Cambridge University Press 2008

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