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arXiv · 1603.09165

Partial transformation groupoids attached to graphs and semigroups

Xin Li
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Abstract

We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crossed products. Both graph C*-algebras and semigroup C*-algebras can be described as C*-algebras attached to partial dynamical systems. As applications, for graphs, we generalize and explain a result of Matsumoto and Matui relating orbit equivalence and Cartan-isomorphism, and for semigroups, we strengthen several structural results for semigroup C*-algebras concerning amenability, nuclearity as well as simplicity of boundary quotients. We also discuss pure infiniteness for partial transformation groupoids arising from graphs and semigroups.

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Xin Li. 2016-03-30. Partial transformation groupoids attached to graphs and semigroups. https://arxiv.org/abs/1603.09165

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