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Keywords = tight groupoid

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16 pages, 278 KiB  
Article
Self-Similar Inverse Semigroups from Wieler Solenoids
by Inhyeop Yi
Mathematics 2020, 8(2), 266; https://doi.org/10.3390/math8020266 - 17 Feb 2020
Viewed by 1902
Abstract
Wieler showed that every irreducible Smale space with totally disconnected local stable sets is an inverse limit system, called a Wieler solenoid. We study self-similar inverse semigroups defined by s-resolving factor maps of Wieler solenoids. We show that the groupoids of germs [...] Read more.
Wieler showed that every irreducible Smale space with totally disconnected local stable sets is an inverse limit system, called a Wieler solenoid. We study self-similar inverse semigroups defined by s-resolving factor maps of Wieler solenoids. We show that the groupoids of germs and the tight groupoids of these inverse semigroups are equivalent to the unstable groupoids of Wieler solenoids. We also show that the C -algebras of the groupoids of germs have a unique tracial state. Full article
(This article belongs to the Special Issue Operator Algebras)
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