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arXiv · 1909.13254

Higher dimensional generalizations of the Thompson groups

Mark V Lawson·Alina Vdovina
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Abstract

We show how to construct a family of groups with simple commutator subgroups from aperiodic 1-vertex, finitely aligned higher rank graphs (which are, in fact, a class of cancellative monoids). Inverse semigroups form the intermediary between these cancellative monoids and the family of groups we are interested in. These groups can naturally be viewed as higher-dimensional generalizations of the classical Thompson groups since the finite direct products of free monoids are examples of the appropriate 1-vertex higher rank graphs.

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Mark V Lawson, Alina Vdovina. 2019-09-29. Higher dimensional generalizations of the Thompson groups. https://arxiv.org/abs/1909.13254

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