The boundary quotient for algebraic dynamical systems
Operator Algebras
2016-11-04 v1 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.
Cite
@article{arxiv.1504.05734,
title = {The boundary quotient for algebraic dynamical systems},
author = {Nathan Brownlowe and Nicolai Stammeier},
journal= {arXiv preprint arXiv:1504.05734},
year = {2016}
}
Comments
23 pages