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arXiv · 1611.01052

Equilibrium states on right LCM semigroup C*-algebras

Zahra Afsar·Nathan Brownlowe·Nadia S. Larsen·Nicolai Stammeier
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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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Zahra Afsar, Nathan Brownlowe, Nadia S. Larsen, Nicolai Stammeier. 2017-06-19. Equilibrium states on right LCM semigroup C*-algebras. https://doi.org/10.1093/imrn%2Frnx162

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