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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| 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 |
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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 |

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