Mesland, B., Sengun, M.H. orcid.org/0000-0002-6210-6877 and Wang, H. (2020) A K-theoretic Selberg trace formula. In: Curto, R.E., Helton, W., Lin, H., Tang, X., Yang, R. and Yu, G., (eds.) Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology. International Workshop on Operator Theory and Applications (IWOTA), 23-27 Jul 2018, Shanghai, China. Operator Theory: Advances and Applications, 278 . Birkhäuser, Cham , pp. 403-424. ISBN 9783030433796
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.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2020. This is an author-produced version of a paper subsequently published in Curto R.E., Helton W., Lin H., Tang X., Yang R., Yu G. (eds) Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology. Operator Theory: Advances and Applications, vol 278. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Trace formula; K-theory; Group C∗-algebra; Uniform lattice |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 26 Apr 2019 10:52 |
Last Modified: | 12 Dec 2021 01:38 |
Status: | Published |
Publisher: | Birkhäuser, Cham |
Series Name: | Operator Theory: Advances and Applications |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-030-43380-2_19 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:145172 |