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  A K-theoretic Selberg trace formula

Mesland, B., Şengün, M. H., & Wang, H. (2020). A K-theoretic Selberg trace formula. In R. E.. Curto, W. Helton, & H. Lin (Eds.), Operator theory, operator algebras and their interactions with geometry and topology: Ronald G. Douglas memorial volume (pp. 403-424). Cham: Birkhäuser.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0007-AD87-E Version Permalink: https://hdl.handle.net/21.11116/0000-0007-AD88-D
Genre: Conference Paper

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arXiv:1904.04728.pdf (Preprint), 255KB
 
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Mesland-Sengun-Hang_A K-Theoretic Selberg Trace Formula_2020.pdf (Publisher version), 563KB
 
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 Creators:
Mesland, Bram1, Author           
Şengün, Mehmet Haluk1, Author           
Wang, Hang, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory, 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 22
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1904.04728
DOI: 10.1007/978-3-030-43380-2_19
 Degree: -

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Title: International Workshop on Operator Theory and Applications (IWOTA)
Place of Event: Shanghai
Start-/End Date: 2018-07-23 - 2018-07-27

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Title: Operator theory, operator algebras and their interactions with geometry and topology : Ronald G. Douglas memorial volume
Source Genre: Proceedings
 Creator(s):
Curto, Raul E ., Editor
Helton, William, Editor
Lin, Huaxin, Editor
Affiliations:
-
Publ. Info: Cham : Birkhäuser
Pages: X, 534 Volume / Issue: - Sequence Number: - Start / End Page: 403 - 424 Identifier: ISBN: 978-3-030-43379-6
ISBN: 978-3-030-43380-2
DOI: 10.1007/978-3-030-43380-2

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Title: Operator theory: advances and applications
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 278 Sequence Number: - Start / End Page: - Identifier: -