Repositorio de producción científica de la Universidad de Sevilla

Computation of centralizers in braid groups and Garside groups


Advanced Search
Opened Access Computation of centralizers in braid groups and Garside groups

Show item statistics
Export to
Author: Gonçalves Soares Franco, Nuno María
González-Meneses López, Juan
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2003
Published in: Revista Matemática Iberoamericana, 19, 367-384
Document type: Article
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 conjugacy problem given by the authors in [9] Franco, N. and Gonzalez-Meneses, J.: Conjugacy problem for braid groups and Garside groups, to appear in Journal of Algebra. Available at, are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2] Anshel, I., Anshel, M. and Goldfeld, D.: An algebraic method for public-key cryptography. Math. Res. Lett. 6 (1999), no. 3-4, 287–291. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.
Cite: Gonçalves Soares Franco, N.M. y González-Meneses López, J. (2003). Computation of centralizers in braid groups and Garside groups. Revista Matemática Iberoamericana, 19, 367-384.
Size: 208.3Kb
Format: PDF


DOI: 10.4171/RMI/352

See editor´s version

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)