On the inverse braid and reflection monoids of type $B$

zbMATH Open1212.20090arXiv0903.0085MaRDI QIDQ5391613

Vladimir Vershinin

Publication date: 6 April 2011

Abstract: There are well known relations between braid groups and symmetric groups, between Artin-Briskorn braid groups and Coxeter groups. Inverse braid monoid the same way is related to the inverse symmetric monoid. In the paper we show that similar relations exist between the inverse braid monoid of type $B$ and the inverse reflection monoid of type $B$. This gives a presentation of the last monoid.

Full work available at URL: https://arxiv.org/abs/0903.0085

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zbMATH Keywords

presentationsCoxeter groupsbraid groupsbraidsreflection groupsgenerators and relationsinverse braid monoidsreflection monoidsinverse symmetric monoids

Mathematics Subject Classification ID

Free semigroups, generators and relations, word problems (20M05) Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Inverse semigroups (20M18)

Related Items (2)

BIRGET–RHODES EXPANSION OF GROUPS AND INVERSE MONOIDS OF MÖBIUS TYPE ⋮ On a Class of Factorizable Inverse Monoids Associated with Braid Groups

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