Higher dimensional generalizations of the Thompson groups via higher rank graphs

Mark V. Lawson; Aidan Sims; Alina Vdovina

doi:10.1016/j.jpaa.2023.107456

Higher dimensional generalizations of the Thompson groups via higher rank graphs

Mark V. Lawson, Aidan Sims, Alina Vdovina

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Abstract

We construct a family of groups from suitable higher rank graphs which are higher dimensional generalizations of the Thompson groups. We introduce group invariants, inspired by the K-theory of C^⁎-algebras, and show that many of our groups are not isomorphic to the Brin-Thompson groups nV, when n ≥ 2 .

Original language	English
Article number	107456
Journal	Journal of Pure and Applied Algebra
Volume	228
Issue number	1
Early online date	5 Jun 2023
DOIs	https://doi.org/10.1016/j.jpaa.2023.107456
Publication status	Published - Jan 2024

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title = "Higher dimensional generalizations of the Thompson groups via higher rank graphs",

abstract = "We construct a family of groups from suitable higher rank graphs which are higher dimensional generalizations of the Thompson groups. We introduce group invariants, inspired by the K-theory of C⁎-algebras, and show that many of our groups are not isomorphic to the Brin-Thompson groups nV, when n ≥ 2 .",

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AB - We construct a family of groups from suitable higher rank graphs which are higher dimensional generalizations of the Thompson groups. We introduce group invariants, inspired by the K-theory of C⁎-algebras, and show that many of our groups are not isomorphic to the Brin-Thompson groups nV, when n ≥ 2 .

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Higher dimensional generalizations of the Thompson groups via higher rank graphs

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