Braids and self-distributivity

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On the dynamics of (left) orderable groups (2007, background): “– A celebrated result by Dehornoy establishes that braid groups Bn are orderable (see for instance [16]).”
Garside Groups and Yang–Baxter Equation (2009, unknown): “We refer the reader to [4, 5] for the definitions of the left lcm and the left and right gcd of two elements.”
Circular groups, planar groups, and the Euler class (2004, background): “Geom etry & Topology M onographs Volum e 7:Proceedingsofthe Casson Fest Pages431{491”
The group of parenthesized braids (2004, background): “By [15], Propositions VI.”
Biquandles and virtual links (2004, background): “These have been called the Wada identities in [5] because of [28], but see also [11] Since the switchS is a bijection there are two more binary operations called the up-bar anddown-baroperations.”
The algebra of strand splitting. I. A braided version of Thompson's group V (2004, background): “See [8] for more information and consequences of the relationship between this law and the ordinary braid groups.”
GROUP ACTIONS ON 1-MANIFOLDS: A LIST OF VERY CONCRETE OPEN QUESTIONS (2017, result): “Building on seminal work of Dehornoy [28], Dubrovina and Dubrovin showed in [40] that Bn admits the disjoint decomposition Bn = 〈 a1, . . . , an−1〉+ ∪ 〈a−11 , . . . , a −1 n−1 〉+ ∪ {id}, where 〈·〉+ stands for the semigroup generated by the corresponding set of elements.”