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Equilibrium states on right LCM semigroup C*-algebras (1611.01052v2)
Published 3 Nov 2016 in math.OA and math.DS
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.