Noncommutative geometry on the Berkovich projective line

Abstract: The Berkovich projective line is an analytic space over a non-Archimedean field. It can also be constructed as an inverse limit of finite rooted trees. We find how to associate $C^*$-algebras generated by partial isometries to the Berkovich line. This allows us to construct several spectral triples on this space. Finally, we show that invariant measures, such as the Patterson-Sullivan measure, can be obtained as certain KMS-states of the crossed product algebra with a subgroup of $PGL_2(C_p)$.

This is a joint work with Masoud Khalkhali.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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