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On parabolic submonoids of a class of singular Artin monoids

Part of: Semigroups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Noelle Antony
Noelle Antony
Affiliation:
School of Mathematics and StatisticsF07The University of SydneyNSW 2006Australia e-mail: [email protected]
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Abstract

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This paper concerns parabolic submonoids of a class of monoids known as singular Artin monoids. The latter class includes the singular braid monoid— a geometric extension of the braid group, which was created for the sole purpose of studying Vassiliev invariants in knot theory. However, those monoids may also be construed (and indeed, are defined) as a formal extension of Artin groups which, in turn, naturally generalise braid groups. It is the case, by van der Lek and Paris, that standard parabolic subgroups of Artin groups are canonically isomorphic to Artin groups. This naturally invites us to consider whether the same holds for parabolic submonoids of singular Artin monoids. We show that it is in fact true when the corresponding Coxeter matrix is of ‘type FC’ hence generalising Corran's result in the ‘finite type’ case.

Keywords

singular Artin monoidsparabolic submonoids.

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 20F36: Braid groups; Artin groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 1 , February 2007 , pp. 29 - 37
Copyright
Copyright © Australian Mathematical Society 2007

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