Conjugacy in relatively extra-large Artin groups

Document Type : Ischia Group Theory 2014

Author

Italy

Abstract

In this work we consider conjugacy of elements and parabolic subgroups‎ ‎in details‎, ‎in a new class of Artin groups‎, ‎introduced in an earlier work‎, ‎which may contain arbitrary parabolic subgroups‎. ‎In particular‎, ‎we find‎ ‎algorithmically minimal representatives of elements in a conjugacy class‎ ‎and also an algorithm to pass from one minimal representative to the others‎.

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K. I. App el and P. E. Schupp (1983). Artin groups and Infinite Coxeter groups. Invent. Math.. 72, 201-220 W. A. Bogley and S. J. Pride (1992). Aspherical Relative Presentations. Proc. Edinburgh Math. Soc. (2). 35, 1-39 R. Charney and L. Paris (2014). Convexity of Parabolic Subgroups in Artin Groups. Bull. London Math. Soc.. 46, 1248-1255 A. J. Duncan, I. V. Kazachkov and V. N. Remeslennikov (2006). Centraliser dimension of partially commutative groups. Geom. Dedicata. 120, 73-97 E. A. El-Rifai and H. R. Morton (1994). Algorithms for p ositive braids. Quart. J. Math. Oxford Ser. (2). 45, 479-497 R. Fenn, D. Rolfsen and J. Zhu (1996). Centralisers in the Braid group and singular braid monoid. Enseign. Math. (2). 42, 75-96 E. Godelle (2007). Artin-Tits groups with CAT(0) Deligne complex. J. Pure Appl. Algebra. 208, 39-52 J. Gonzalez-Meneses and B. Wiest (2004). On the Structure of the centralizers of a braid. Ann. Sci. Ecole Norm. Sup. (4). 37, 729-757 V. A. Grinblatt (1986). On normalisers of Artin groups. Amer. Math. Soc. Transl.. 132, 89-98 A. Juhasz (1991). Fusion in Artin Groups I. J. London Math. Soc. (2). 44, 287-300 A. Juhasz On a class of Artin groups. Submitted. R. C. Lyndon and P. E. Schupp (2001). Combinatorial Group Theory. Springer Verlag. L. Paris (1997). Parab olic subgroups of Artin groups. J. Algebra. 196, 369-399 L. Paris (1997). Centralizers of Parabolic subgroups of Artin groups of type A_l , B_l and P_l. J. Algebra. 196, 400-435 D. Rolfsen (1997). Braid subgroups normalisers, commensurators and induced representations. Invent. Math.. 130, 575-587
Volume 4, Issue 3 - Serial Number 3
Proceedings of the Ischia Group Theory 2014-Part III.
September 2015
Pages 77-117
  • Receive Date: 13 March 2015
  • Revise Date: 30 September 2015
  • Accept Date: 30 September 2015
  • Published Online: 01 September 2015