Semigroups of local homeomorphisms and interaction groups
By R. Exel, J. Renault. Ergodic Theory and Dynamical Systems, 2006
58 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6df6b8771e2afb07216b1e5385bdd8914f7a1218
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Ample groupoids: equivalence, homology, and Matui's HK conjecture (2018, background): “2sometimes referred to as a transformation groupoid (see [18])”
- Semicrossed Products of Operator Algebras by Semigroups (2014, methodology): “Before we proceed to the presentation of the main results we mention that there is a substantial literature on the examination of semigroup actions that involves the existence of transfer operators, e.g., the works of Brownlowe-Raeburn [17], Brownlowe-Raeburn-Vittadello [18], Exel [46], Exel-Renault”