J. Aust. Math. Soc.  82 (2007), 29-37
On parabolic submonoids of a class of singular Artin monoids

Noelle Antony
  School of Mathematics and Statistics, F07
  The University of Sydney
  NSW 2006

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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