Quantum Statistical Mechanics of $\mathbb{Q}$-lattices and noncommutative geometry
Operator Algebras
2008-08-22 v2 Number Theory
Abstract
After recalling some basic notions of quantum statistical mechanics, we explain the Bost-Connes system that relates the structure of the maximal abelian extension of to the space of \kms states of a \cs-dynamical system. Afterwards, we study briefly the Connes-Marcolli -system as a generalization of the former system.
Keywords
Cite
@article{arxiv.0808.1767,
title = {Quantum Statistical Mechanics of $\mathbb{Q}$-lattices and noncommutative geometry},
author = {Vahid Shirbisheh},
journal= {arXiv preprint arXiv:0808.1767},
year = {2008}
}
Comments
These are (updated version of) my notes of the talk given as the second part of the author comprehensive examination at the University of Western Ontario in May 2005. Some recent developments have been considered and some new references have been added. (10 pages)