A K-theoretic Selberg trace formula
Number Theory
2019-10-29 v2 K-Theory and Homology
Operator Algebras
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.
Keywords
Cite
@article{arxiv.1904.04728,
title = {A K-theoretic Selberg trace formula},
author = {Bram Mesland and Mehmet Haluk Sengun and Hang Wang},
journal= {arXiv preprint arXiv:1904.04728},
year = {2019}
}
Comments
Extended the introduction and added a couple of extra remarks in Section 4