The boundary quotient for algebraic dynamical systems

Abstract

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.

23 pages

References in corpus (2)

• C*-algebras associated to product systems of Hilbert bimodules
• C*-Algebras of algebraic dynamical systems and right LCM semigroups

Cited by in corpus (8)

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• $C^{\ast }$-algebras of right LCM monoids and their equilibrium states
• Graph products and the absence of property (AR)
• A boundary quotient diagram for right LCM semigroups
• Algebraic actions I. C*-algebras and groupoids