Equilibrium states on right LCM semigroup C*-algebras

Abstract

We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of $C^{\ast }$-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers the previous case studies on $\mathbb{N}⋊{\mathbb{N}}^{\times }$, dilation matrices, self-similar actions, and Baumslag-Solitar monoids. At the same time, it provides new results for large classes of right LCM semigroups, including those associated to algebraic dynamical systems.

43 pages, to appear in Int. Math. Res. Not

References in corpus (4)

• Equilibrium states on operator algebras associated to self-similar actions of groupoids on graphs
• C*-Algebras of algebraic dynamical systems and right LCM semigroups
• The boundary quotient for algebraic dynamical systems
• Graph products and the absence of property (AR)

Cited by in corpus (8)

• C*-Algebras of algebraic dynamical systems and right LCM semigroups
• The inner structure of boundary quotients of right LCM semigroups
• The groupoid approach to equilibrium states on right LCM semigroup C*-algebras
• $C^{\ast }$-algebras of right LCM monoids and their equilibrium states
• Graph products and the absence of property (AR)
• Boundary Quotient C*-algebras of Products of Odometers
• Normal coactions extend to the C*-envelope
• Skew products of finitely aligned left cancellative small categories and Cuntz-Krieger algebras