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arXiv · 1904.04728

A K-theoretic Selberg trace formula

Bram Mesland·Mehmet Haluk Sengun·Hang Wang
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Abstract

Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test functions. In this paper we present a cohomological interpretation of the trace formula involving the K-theory of the maximal group C*-algebras of G and H. As an application, we exploit the role of group C*-algebras as recipients of higher indices of elliptic differential operators and we obtain the index theoretic version of the Selberg trace formula developed by Barbasch and Moscovici from ours.

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Bram Mesland, Mehmet Haluk Sengun, Hang Wang. 2019-04-09. A K-theoretic Selberg trace formula. https://arxiv.org/abs/1904.04728

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