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arXiv · 1902.02674

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

Nathan Brownlowe·Nadia S. Larsen·Jacqui Ramagge·Nicolai Stammeier
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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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Nathan Brownlowe, Nadia S. Larsen, Jacqui Ramagge, Nicolai Stammeier. 2019-02-07. $C^*$-algebras of right LCM monoids and their equilibrium states. https://arxiv.org/abs/1902.02674

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