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Explicit presentations for the dual braid monoids. (English. Abridged French version) Zbl 1020.20027

Summary: Birman, Ko and Lee have introduced a new monoid \({\mathcal B}_n^*\) – with an explicit presentation – whose group of fractions is the \(n\)-strand braid group \({\mathcal B}_n\). Building on a new approach by Digne, Michel and himself, Bessis has defined a dual braid monoid for every finite Coxeter type Artin-Tits group extending the type \(A\) case. Here, we give an explicit presentation for this dual braid monoid in the case of types \(B\) and \(D\), and we study the combinatorics of the underlying Garside structures.

MSC:

20F36 Braid groups; Artin groups
20M05 Free semigroups, generators and relations, word problems

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References:

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