Computation of Centralizers in Braid groups and Garside Groups

Details Computation of Centralizers in Braid groups and Garside Groups Computation of Centralizers in Braid groups and Garside Groups

2002-01-25

arxiv.org/abs/math/0201243v2

Mathematics

Geometric Topology

The algorithm has been improved by using the Summit Class, instead of the conjugacy class of the element under study. The word

Scientific paper

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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