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⋊N×, 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. The final version of this research has been published in International Mathematics Research Notices. © 2017 Oxford University Pres