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Character rigidity for special linear groups

Jesse Peterson and Andreas Thom

Abstract

In this paper we study characters on special linear groups SLn(R), where R is either an infinite field or the localization of an order in a number field. We give several applications to the theory of measure-preserving actions, operator-algebraic superrigidity, and almost homomorphisms.

Funding source: National Science Foundation

Award Identifier / Grant number: DMS-1201565

Funding source: European Research Council

Award Identifier / Grant number: 277728

Funding statement: J. Peterson is supported by NSF Grant DMS-1201565, and a grant from the Alfred P. Sloan Foundation. A. Thom is supported by ERC Grant 277728.

We want to thank Miklós Abért for motivating discussions and sharing a preliminary version of [‘A strong simplicity property for projective special linear groups’, preprint] with us, and Tim Netzer for discussions about Theorem 5.2. A. Thom wants to thank Uri Bader for interesting discussions about a first version of this paper. This work was started when J. Peterson visited Universität Leipzig in September 2012, he is grateful for their hospitality. We thank the unknown referee for careful proof-reading and many helpful comments.

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Received: 2013-6-3
Revised: 2014-2-4
Published Online: 2014-3-11
Published in Print: 2016-7-1

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