The Group of Self-distributivity Is Bi-orderable

نویسنده

  • Patrick DEHORNOY
چکیده

We prove that the group of left self-distributivity, a cousin of Thompson’s group F and of Artin’s braid group B∞ 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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تاریخ انتشار 2003