A K-Theoretic Selberg Trace Formula

Bram Mesland, Mehmet Haluk Şengün, Hang Wang

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

Let G be a semisimple Lie group and Γ 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 L2(Γ∖G) associated to test functions f ∈ Cc(G). 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 Γ. 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.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Pages403-424
Number of pages22
DOIs
StatePublished - 2020

Publication series

NameOperator Theory: Advances and Applications
Volume278
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Group C-algebra
  • K-theory
  • Trace formula
  • Uniform lattice

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