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Conjugacy in singular Artin monoids

Part of: Semigroups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Ruth Corran
Ruth Corran
Affiliation:
Institut de Géométrie, Algèbre et Topologie, Bâtiment BCH, École Polytechnique Fédérale de Lausanne, CH-1015, Switzerland, e-mail: [email protected]
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Abstract

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We define a notion of conjugacy in singular Artin moniods, and solve the corresponding conjugacy problem for finite types. We sgiw that this definition is appropriate to describe type (1) singular Markov moves on singular braids. Parabolic submonoids of singular Artin monoids are defined and, in finite type, are shown to be singular Artin monoids. Solutions to conjugacy-type problems of parabolic submonoids are described. Geometric objects defined by Fenn, Rolfsen and Zhu, called (j, k)-bands, are algebraically characterised, and a procedure is given which determines when a word represents a (j, k)-band.

MSC classification

Secondary: 20F36: Braid groups; Artin groups 20M05: Free semigroups, generators and relations, word problems 20F05: Generators, relations, and presentations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 2 , October 2005 , pp. 183 - 212
Copyright
Copyright © Australian Mathematical Society 2005

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