$C^{\ast }$-algebras of right LCM monoids and their equilibrium states

Abstract

We study the internal structure of $C^{\ast }$-algebras of right LCM monoids by means of isolating the core semigroup $C^{\ast }$-algebra as the coefficient algebra of a Fock-type module on which the full semigroup $C^{\ast }$-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 $C^{\ast }$-algebra, and provide sufficient conditions for uniqueness of the KMS${}_{\beta }$-state at inverse temperature $\beta$ in a critical interval.

39 pages

References in corpus (4)

• The inner structure of boundary quotients of right LCM semigroups
• Preferred traces on C*-algebras of self-similar groupoids arising as fixed points
• Reconstructing the Bost--Connes semigroup actions from K-theory
• Regular Dilation and Nica-covariant Representation on Right LCM Semigroups

Cited by in corpus (1)

• The groupoid approach to equilibrium states on right LCM semigroup C*-algebras