Commentarii Mathematici Helvetici

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Volume 76, Issue 1, 2001, pp. 161–182
DOI: 10.1007/s000140050154

Published online: 2001-03-31

The group of self-distributivity is bi-orderable

Patrick Dehornoy[1]

(1) Université de Caen, France

We prove that the group of left self-distributivity, a cousin of Thompson's group F and of Artin's braid group $ B_\infty $ that describes the geometry of the identity x(yz) = (xy)(xz), admits a bi-invariant linear ordering. To this end, we define a partial action of this group on finite binary trees that preserves a convenient linear ordering.

Keywords: Ordered groups, groups acting on trees, self-distributivity, Thompson's groups

Dehornoy Patrick: The group of self-distributivity is bi-orderable. Comment. Math. Helv. 76 (2001), 161-182. doi: 10.1007/s000140050154