Conjugacy in singular Artin monoids

• Autores: Ruth Corran
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 79, Nº 2, 2005, págs. 183-212
• Idioma: inglés
• DOI: 10.1017/s1446788700010442
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• Resumen

  • We define a notion of conjugacy in singular Artin monoids, and solve the corresponding conjugacy problem for finite types. We show 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.