English

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.

Keywords

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

R2 v1 2026-06-22T09:20:22.626Z