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Semigroups of local homeomorphisms and interaction groups

Published online by Cambridge University Press:  01 December 2007

R. EXEL  and
J. RENAULT
R. EXEL
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Brazil (email: exel@mtm.ufsc.br)
J. RENAULT
Affiliation:
Départment de Mathématiques, Université d’Orléans, 45067 Orléans, France (email: Jean.Renault@univ-orleans.fr)
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Abstract

Given a semigroup of surjective local homeomorphisms on a compact space X we consider the corresponding semigroup of *-endomorphisms on C(X) and discuss the possibility of extending it to an interaction group, a concept recently introduced by the first named author. We also define a transformation groupoid whose C*-algebra turns out to be isomorphic to the crossed product algebra for the interaction group. Several examples are considered, including one which gives rise to a slightly different construction and should be interpreted as being the C*-algebra of a certain polymorphism.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1737 - 1771
Copyright
Copyright © Cambridge University Press 2007

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