Higher dimensional generalizations of the Thompson groups
Rings and Algebras
2020-04-07 v2 Group Theory
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.
Cite
@article{arxiv.1909.13254,
title = {Higher dimensional generalizations of the Thompson groups},
author = {Mark V Lawson and Alina Vdovina},
journal= {arXiv preprint arXiv:1909.13254},
year = {2020}
}
Comments
Revised version of paper. Many minor typos corrected