Abstract.
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.
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Received: September 10, 1999, revised version: June 5, 2000
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Dehornoy, P. The group of self-distributivity is bi-orderable. Comment. Math. Helv. 76, 161–182 (2001). https://doi.org/10.1007/s000140050154
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DOI: https://doi.org/10.1007/s000140050154