Computation of Centralizers in Braid groups and Garside groups

Revista Matematica Iberoamericana

Volumn 19, Issue 2, 2003, Pages 367-384

  Franco, Nuno ^a   González Meneses, Juan ^b  

^a UNIVERSITY OF ÉVORA   (Portugal)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Braid group; Centralizer; Cryptography; Garside group

Indexed keywords

EID: 0141942095     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/352     Document Type: Article

References (17)

1. ARTIN, E.: Theory of braids. Annals of Math. 48 (1946), 101-126.
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.
3. BIRMAN, J., KO, K. H. AND LEE, S. J.: A new approach to the word and conjugacy problems in the braid groups. Adv. Math. 139 (1998), no. 2, 322-353.
4. BIRMAN, J., KO, K. H. AND LEE, S. J.: The infimum, supremum and geodesic length of a braid conjugacy class. Adv. Math. 164 (2001), 41-56.
5. BRIESKORN, E. AND SAITO, K.: Artin-Gruppen und Coxeter-Gruppen. Invent. Math. 17 (1972), 245-271.
6. DEHORNOY, P.: Groupes de Garside. Ann. Sci. École Norm. Sup. (4) 35 (2002), 267-306.
7. DEHORNOY, P. AND PARIS, L.: Gaussian groups and Garside groups, two generalizations of Artin groups. Proc. London Math. Soc. 79 (1999), no. 3, 569-604.
8. ELRIFAI, E. A. AND MORTON, H. R.: Algorithms for positive braids. Quart. J. Math. Oxford 45 (1994), 479-497.
9. FRANCO, N. AND GONZÁLEZ-MENESES, J.: Conjugacy problem for braid groups and Garside groups, to appear in Journal of Algebra. Available at http://arxiv.org/math.GT/0112310
10. GARSIDE, F. A.: The braid group and other groups. Quart, J. Math. Oxford 20 (1969), 235-154.
11. GONZÁLEZ-MENESES, J. AND WIEST, B.: On the structure of the centralizer of a braid. In preparation.
12. KO, K. H., LEE, S.J., CHEON, J.H., HAN, J.W., KANG, J. AND PARK, C.: New public-key cryptosystem using braid groups. In Advances in cryptology-CRYPTO 2000 (Santa Barbara, CA), 166-183. Lecture Notes in Comput. Sci. 1880, Springer, Berlin, 2000.
13. LYNDON, R. C. AND SCHUPP, P.E.: Combinatorial group theory. Reprint of the 1977 edition. Classics in Mathematics, Springer-Verlag, Berlin, 2001.
14. MAKANIN, G. S.: The normalizes in the braid group. Mat. Sb. (N. S.) 86 (128) (1971), 171-179.
15. PICANTlN, M.: Petits groupes gaussiens. Ph. D. Thesis, Université de Caen, 2000.
16. PICANTIN, M.: The conjugacy problem in small Gaussian groups. Comm. Algebra 29 (2001), no. 3, 1021-1039.
17. THURSTON, W. P.: Braid Groups, Chapter 9 of Word processing in groups, D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson and W. P. Thurston. Jones and Bartlett Publishers, Boston, MA, 1992.