The boundary quotient for algebraic dynamical systems. (English) Zbl 1358.46065
Summary: We introduce the notion of accurate foundation sets and the accurate refinement property for right LCM semigroups. For right LCM semigroups with this property, we derive a more explicit presentation of the boundary quotient. In the context of algebraic dynamical systems, we also analyse finiteness properties of foundation sets which lead us to a very concrete presentation. Based on Starling’s recent work, we provide sharp conditions on certain algebraic dynamical systems for pure infiniteness and simplicity of their boundary quotient.
MSC:
| 46L55 | Noncommutative dynamical systems |
| 37A55 | Dynamical systems and the theory of \(C^*\)-algebras |
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