Convergence and limits of linear representations of finite groups

Elek, Gabor (2016) Convergence and limits of linear representations of finite groups. Journal of Algebra, 450. pp. 588-615. ISSN 0021-8693

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Abstract

Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in continuous algebras. We show that under a certain integrality condition, the algebras above are skew fields. Our main result is the extension of Schramm's characterization of hyperfiniteness to linear representations.

Item Type:

Journal Article

Journal or Publication Title:

Journal of Algebra

Additional Information:

This is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, 450, 2016 DOI: 10.1016/j.jalgebra.2015.11.023

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2602

Subjects:

?? linear representationsamenability soficity continuous ringsskew fieldsalgebra and number theory ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

76909

Deposited By:

ep_importer_pure

Deposited On:

27 Nov 2015 15:58

Refereed?:

Yes

Published?:

Published

Last Modified:

27 Oct 2024 00:13

URI:

https://eprints.lancs.ac.uk/id/eprint/76909