Bruce, C. (2021) Phase transitions on C*-algebras from actions of congruence monoids on rings of algebraic integers. International Mathematics Research Notices, 2021(5), pp. 3653-3697. (doi: 10.1093/imrn/rnaa056)
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Abstract
We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each β∈[1,2], there is a unique KMSβ state, and we prove that it is a factor state of type III1. There are phase transitions at β=2 and β=∞ involving a quotient of a ray class group. Our computation of KMS and ground states generalizes the results of Cuntz, Deninger, and Laca for the full ax+b-semigroup over a ring of integers, and our type classification generalizes a result of Laca and Neshveyev in the case of the rational numbers and a result of Neshveyev in the case of arbitrary number fields.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Bruce, Dr Chris |
| Authors: | Bruce, C. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | International Mathematics Research Notices |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| ISSN (Online): | 1687-0247 |
| Published Online: | 21 April 2020 |
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