Artin groups of XXL type are isomorphic to their dual Artin groups for any Coxeter element.
A dual braid monoid for the free group
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abstract
We construct a quasi-Garside monoid structure for the free group. This monoid should be thought of as a dual braid monoid for the free group, generalising the constructions by Birman-Ko-Lee and by the author of new Garside monoids for Artin groups of spherical type. Conjecturally, an analog construction should be available for arbitrary Artin groups and for braid groups of well-generated complex reflection groups.
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math.GR 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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The dual Artin isomorphism for Artin groups of XXL type
Artin groups of XXL type are isomorphic to their dual Artin groups for any Coxeter element.