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

Brownlowe, Nathan; Larsen, Nadia S.; Ramagge, Jacqui; Stammeier, Nicolai

Abstract

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.

Citation

Brownlowe, N., Larsen, N. S., Ramagge, J., & Stammeier, N. (2020). $C^*$-algebras of right LCM monoids and their equilibrium states. Transactions of the American Mathematical Society, 373(7), 5235-5273. https://doi.org/10.1090/tran/8097

• Journal Article Type: Article
• Online Publication Date: Apr 28, 2020
• Publication Date: 2020-07
• Deposit Date: Jul 9, 2020
• Publicly Available Date: Jul 9, 2020
• Journal: Transactions of the American Mathematical Society
• Print ISSN: 0002-9947
• Electronic ISSN: 1088-6850
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 373
• Issue: 7
• Pages: 5235-5273
• DOI: https://doi.org/10.1090/tran/8097
• Public URL: https://durham-repository.worktribe.com/output/1298174