The $\mathrm{GL}_n$-Connes-Marcolli Systems

Yunyi Shen

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arXiv · 1609.08727

The $\mathrm{GL}_n$-Connes-Marcolli Systems

Yunyi Shen

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Abstract

In this paper, we generalize the results of Laca, Larsen, and Neshveyev on the $\mathrm{GL}_2$-Connes-Marcolli system to the $\mathrm{GL}_n$ systems. We introduce the $\mathrm{GL}_n$-Connes-Marcolli systems and discuss the question of the existence and the classification of KMS equilibrium states at different inverse temperatures $β$. In particular, using an ergodicity argument, we prove that in the range $n-1 <β\leq n$, there is only one KMS state. We show that there are no KMS states for $β n$.

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BibTeX RIS

Yunyi Shen. 2016-09-28. The $\mathrm{GL}_n$-Connes-Marcolli Systems. https://arxiv.org/abs/1609.08727

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