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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Authors: Nathan Brownlowe, Nadia S. Larsen, Jacqui Ramagge and Nicolai Stammeier
Journal: Trans. Amer. Math. Soc. 373 (2020), 5235-5273
MSC (2010): Primary 46L05; Secondary 46L30, 20M10
DOI: https://doi.org/10.1090/tran/8097
Published electronically: April 28, 2020
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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^*$-algebra and provide sufficient conditions for uniqueness of the KMS$ _\beta $-state at inverse temperature $ \beta $ in a critical interval.


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Additional Information

Nathan Brownlowe
Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
Email: Nathan.Brownlowe@sydney.edu.au

Nadia S. Larsen
Affiliation: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, NO-0316 Oslo, Norway
Email: nadiasl@math.uio.no

Jacqui Ramagge
Affiliation: Faculty of Science, Durham University, Durham DH1 3LE, United Kingdom
Email: jacqui.ramagge@durham.ac.uk

Nicolai Stammeier
Affiliation: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, NO-0316 Oslo, Norway
Email: n.stammeier@gmail.com

DOI: https://doi.org/10.1090/tran/8097
Received by editor(s): May 10, 2019
Received by editor(s) in revised form: January 9, 2020
Published electronically: April 28, 2020
Additional Notes: This research was supported by the Research Council of Norway (RCN FRIPRO 240362), the Australian Research Council (ARC DP170101821), and the Trond Mohn Foundation through the project “Pure Mathematics in Norway”.
Article copyright: © Copyright 2020 American Mathematical Society