Convergence and limits of linear representations of finite groups

Elek, Gábor (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. © 2015 Elsevier Inc.

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