Computation of Centralizers in Braid groups and Garside Groups

2002/01/25 by Nuno Franco, Franco, Nuno, Juan Gonzalez-Meneses +1 · 1 citation
Mathematics · #20F10 #20F36 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F10 #msc:20F36

paper · pdf · doi:10.48550/arxiv.math/0201243

The algorithm has been improved by using the Summit Class, instead of the conjugacy class of the element under study. The word "normalizer" has been replaced by "centralizer". 14 pages, 4 figures

arxiv created 2002/12/10 · arxiv updated 2009/11/30

Abstract

We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conugacy problem given by the authors in a previous paper, are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.

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