English

Convergence and limits of linear representations of finite groups

Rings and Algebras 2015-11-20 v5 Group Theory

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.

Keywords

Cite

@article{arxiv.1406.5032,
  title  = {Convergence and limits of linear representations of finite groups},
  author = {Gabor Elek},
  journal= {arXiv preprint arXiv:1406.5032},
  year   = {2015}
}

Comments

Final version. To appear in the Journal of Algebra