Rights statement: 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
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Convergence and limits of linear representations of finite groups
AU - Elek, Gabor
N1 - 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
PY - 2016/3/16
Y1 - 2016/3/16
N2 - 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.
AB - 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.
KW - linear representations
KW - amenability
KW - soficity
KW - continuous rings
KW - skew fields
U2 - 10.1016/j.jalgebra.2015.11.023
DO - 10.1016/j.jalgebra.2015.11.023
M3 - Journal article
VL - 450
SP - 588
EP - 615
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -