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Noncommutative geometry of groups like Γ0(N)

2013/03/21 by Jorge Plazas, Plazas, Jorge · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Primary 58B34 #Secondary 11F06

paper · pdf · doi:10.48550/arxiv.1303.5168

openalex publication_date 2013/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Connes-Marcolli GL2-system can be represented on the Big Picture, a combinatorial gadget introduced by Conway in order to understand various results about congruence subgroups pictorially. In this representation the time evolution of the system is implemented by Conway's distance between projective classes of commensurable lattices. We exploit these results in order to associate quantum statistical mechanical systems to congruence subgroups in a way appropriate for the study of monstrous moonshine.

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