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Semigroups of local homeomorphisms and interaction groups

Ruy Exel·Jean Renault
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Abstract

Given a semigroup of 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. Under suitable hypotheses we may 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.

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Ruy Exel, Jean Renault. 2006-10-10. Semigroups of local homeomorphisms and interaction groups. https://arxiv.org/abs/math/0608589

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