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

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

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Authors

Nathan Brownlowe

Nadia S. Larsen

Nicolai Stammeier



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 Mar 29, 2024
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

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