A K-theoretic Selberg trace formula

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

Authors/Creators:	Mesland, B. Sengun, M.H. https://orcid.org/0000-0002-6210-6877 Wang, H.
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:	Published (online): 12 December 2020 Published: 12 December 2020
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:	https://doi.org/10.1007/978-3-030-43380-2_19
Related URLs:	arXiv URL

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A K-theoretic Selberg trace formula

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