$C^*$-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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- 10.48550/arXiv.1902.02674
- arXiv:
- arXiv:1902.02674
- Bibcode:
- 2019arXiv190202674B
- Keywords:
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- Mathematics - Operator Algebras;
- Mathematics - Dynamical Systems;
- 46L30 (Primary);
- 46L55;
- 20M30 (Secondary)
- E-Print:
- 39 pages