Semigroups of local homeomorphisms and interaction groups

Details Semigroups of local homeomorphisms and interaction groups Semigroups of local homeomorphisms and interaction groups

2006-08-23

arxiv.org/abs/math/0608589v2

Ergodic Theory Dynam. Systems, 27 (2007), 1737-1771

Mathematics

Operator Algebras

35 pages, no figures. Section 14 added to include an example of commuting endomorphisms not admiting a non-zero coherent cocyc

Scientific paper

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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