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 N x Nx, dilation matrices, self-similar actions, and Baumslag-Solitar monoids. At the same time, it provides new results for right LCM semigroups associated to algebraic dynamical systems.