The boundary quotient for algebraic dynamical systems

Authors

Nathan Brownlowe, University of WollongongFollow
Nicolai Stammeier, University of Oslo

RIS ID

105709

Publication Details

Brownlowe, N. & Stammeier, N. (2016). The boundary quotient for algebraic dynamical systems. Journal of Mathematical Analysis and Applications, 438 (2), 772-789.

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.