The dual braid monoid |
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Authors: | David Bessis |
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Institution: | Institut Girard Desargues, CNRS UMR 5028, Université Lyon 1, 21 avenue Claude Bernard, 69622 Villeurbanne Cedex, France |
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Abstract: | We study a new monoid structure for Artin groups associated with finite Coxeter systems. Like the classical positive braid monoid, the new monoid is a Garside monoid. We give several equivalent constructions: algebraically, the new monoid arises when studying Coxeter systems in a “dual” way, replacing the pair (W,S) by (W,T), with T the set of all reflections; geometrically, it arises when looking at the reflection arrangement from a certain basepoint. In the type A case, we recover the monoid constructed by Birman, Ko and Lee. |
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