Equilibrium states on right LCM semigroup C*-algebras
  We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of $C^*$-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 $\mathbb{N} \rtimes \mathbb{N}^\times$, 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. 
Zahra Afsar, Nathan Brownlowe, Nadia S. Larsen, and Nicolai Stammeier
math.OA math.DS