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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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:
?? linear representationsamenability soficity continuous ringsskew fieldsalgebra and number theory ??
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Deposited On:
27 Nov 2015 15:58
Last Modified:
26 Jan 2024 01:18