$C*$-algebras of right LCM monoids and their equilibrium states

We study the internal structure of C-algebras of right LCM monoids by means of isolating the core semigroup C-algebra as the coecient 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 sucient conditions for uniqueness of the KMS-state at inverse temperature in a critical interval.