Quantum Statistical Mechanics of $\mathbb{Q}$-lattices and noncommutative geometry

Details Quantum Statistical Mechanics of $\mathbb{Q}$-lattices and noncommutative geometry Quantum Statistical Mechanics of $\mathbb{Q}$-lattices and noncommutative geometry

2008-08-13

arxiv.org/abs/0808.1767v2

Mathematics

Operator Algebras

These are (updated version of) my notes of the talk given as the second part of the author comprehensive examination at the Un

Scientific paper

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 $\mathbb{Q}$ to the space of \kms states of a
\cs-dynamical system. Afterwards, we study briefly the Connes-Marcolli
$\text{GL}_2$-system as a generalization of the former system.

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