J. Aust. Math. Soc.
82 (2007), 2937

On parabolic submonoids of a class of singular Artin monoids

Noelle Antony
School of Mathematics and Statistics, F07
The University of Sydney
NSW 2006
Australia
noellea@maths.usyd.edu.au



Abstract

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.

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