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

2019/02/07 by Nathan Brownlowe, Brownlowe, Nathan, Nadia S. Larsen +5
Computer Science · Mathematics · #20M30 (Secondary) #46L30 (Primary) #46L55 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1902.02674

openalex publication_date 2019/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_β-state at inverse temperature β in a critical interval.

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