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arXiv · 0808.1767

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

Vahid Shirbisheh
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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 $\mathbb{Q}$ 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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Vahid Shirbisheh. 2008-08-21. Quantum Statistical Mechanics of $\mathbb{Q}$-lattices and noncommutative geometry. https://arxiv.org/abs/0808.1767

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