Convergence and limits of linear representations of finite groups

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• 作者：Gá ; bor Elek ^{g.elek@lancaster.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20F99 ; 16E50
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：450
• 期：Complete
• 页码：588-615
• 全文大小：463 K

文摘

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.