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Noncommutative Geometry of Groups Like Γ0(N)

  • Jorge PlazasEmail author
Research Articles
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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 GL2-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. This work is motivated by the study of congruence subgroups and their principal moduli in connection with monstrous moonshine.

Key words

commensurability of Q-lattices congruence subgroups 
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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Pontificia Universidad JaverianaBogotá D.C.Colombia

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