\(C^*\)-algebras of right LCM monoids and their equilibrium states

Abstract

We study the internal structure of \(C^*\)-algebras of right LCM monoids by means of isolating the core semigroup \(C^*\)-algebra as the coefficient algebra of a Fock-type module on which the full semigroup \(C^*\)-algebra admits a left action. If the semigroup has a generalised scale, we classify the KMS-states for the associated time evolution on the semigroup \(C^*\)-algebra, and provide sufficient conditions for uniqueness of the KMS\(_\beta\)-state at inverse temperature \(\beta\) in a critical interval.