The $\mathrm{GL}_n$-Connes-Marcolli Systems
Operator Algebras
2016-09-29 v1
Abstract
In this paper, we generalize the results of Laca, Larsen, and Neshveyev on the -Connes-Marcolli system to the systems. We introduce the -Connes-Marcolli systems and discuss the question of the existence and the classification of KMS equilibrium states at different inverse temperatures . In particular, using an ergodicity argument, we prove that in the range , there is only one KMS state. We show that there are no KMS states for and not an integer, while we construct KMS states for integer values of in the range , and we classify extremal KMS states for .
Cite
@article{arxiv.1609.08727,
title = {The $\mathrm{GL}_n$-Connes-Marcolli Systems},
author = {Yunyi Shen},
journal= {arXiv preprint arXiv:1609.08727},
year = {2016}
}