## Equilibrium states for right LCM semigroup $$C^*$$-algebras

### Zahra Afsar, Nathan Brownlowe, Nadia S. Larsen, Nicolai Stammeier

#### Abstract

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.

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 Thursday, November 17, 2016