Bruce, C. , Laca, M. and Takeishi, T. (2021) Partition functions as C*-dynamical invariants and actions of congruence monoids. Communications in Mathematical Physics, 382(2), pp. 1165-1203. (doi: 10.1007/s00220-020-03859-1)
Full text not currently available from Enlighten.
Abstract
We study KMS states for the C*-algebras of ax+b-semigroups of algebraic integers in which the multiplicative part is restricted to a congruence monoid, as in recent work of Bruce. We realize the extremal low-temperature KMS states as generalized Gibbs states in concrete representations induced from extremal traces of certain group C*-algebras. We use these representations to compute the type of extremal KMS states and we determine explicit partition functions for those of type I. The resulting collection of partition functions is an invariant for equivariant isomorphism classes of C*-dynamical systems, which produces further invariants through the analysis of the topological structure of the KMS state space. We use this to characterize several features of the underlying number field and congruence monoid. In most cases our systems have infinitely many type I factor KMS states and at least one type II factor KMS state at the same inverse temperature and there are infinitely many partition functions. In order to deal with this multiplicity, we establish, in the context of general C*-dynamical systems, a precise way to associate partition functions to extremal type I KMS states. This discussion of partition functions for C*-dynamical systems may be of interest by itself and is likely to have applications in other contexts so we include it in a self-contained initial section that is partly expository and is independent of the number-theoretic background.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Bruce, Dr Chris |
| Authors: | Bruce, C., Laca, M., and Takeishi, T. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | Communications in Mathematical Physics |
| Publisher: | Springer |
| ISSN: | 0010-3616 |
| ISSN (Online): | 1432-0916 |
| Published Online: | 19 September 2020 |
| Related URLs: |
University Staff: Request a correction | Enlighten Editors: Update this record
Deposit and Record Details
Deposit and Record Details