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A generalized type semigroup and dynamical comparison

Part of: Topological dynamics Selfadjoint operator algebras

Published online by Cambridge University Press:  13 April 2020

XIN MA
XIN MA*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA email xma29@buffalo.edu Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260, USA
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Abstract

In this paper, we construct and study a semigroup associated to an action of a countable discrete group on a compact Hausdorff space that can be regarded as a higher dimensional generalization of the type semigroup. We study when this semigroup is almost unperforated. This leads to a new characterization of dynamical comparison and thus answers a question of Kerr and Schafhauser. In addition, this paper suggests a definition of comparison for dynamical systems in which neither the acting group is necessarily amenable nor the action is minimal.

Keywords

operator algebrastopological dynamicsgeneralized type semigroupdynamical comparison

MSC classification

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Secondary: 46L35: Classifications of $C^*$-algebras
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 7 , July 2021 , pp. 2148 - 2165
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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