Gaussian groups and Garside groups, two generalisations of Artin groups

Proceedings of the London Mathematical Society

Volumn 79, Issue 3, 1999, Pages 569-604

  Dehornoy, Patrick ^a   Paris, Luis ^b  

^a UNIVERSITÉ DE CAEN   (France)

^b UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000850020     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611599012071     Document Type: Article

References (32)

1. S. I. ADJAN, 'Defining relations and algorithmic problems for groups and semigroups', Proc. Steklov Inst. Math. 85 (1996).
2. S. I. ADJAN, 'Fragments of the word Delta in a braid group', Mat. Zam. Acad. Sci. SSSR 36-1 (1984) 25-34 (Russian),
3. Math. Notes Acad. Sci. USSR 36-1 (1984) 505-510 (English).
4. J. BIRMAN, K. H. Ko and S. J. LEE, 'A new approach to the word problem in the braid groups', Adv. in Math. 139 (1998) 322-353.
5. N. BOURBAKI, Groupes et algèbres de Lie, Chapitres 4, 5 et 6 (Hermann, Paris, 1968).
6. E. BRIESKORN and K. SAITO, 'Artin-Gruppen und Coxeter-Gruppen', Invent. Math. 17 (1972) 245-271.
7. M. BROUÉ, G. MALLE and R. ROUQUIER, 'Complex reflection groups, braid groups, Hecke algebras', J. Reine Angew. Math. 500 (1998) 127-190.
8. M. BROUÉ and J. MICHEL, 'Sur certains éléments réguliers des groupes de Weyl et les variétés de Deligne-Lusztig associées', Finite reductive groups, Progress in Mathematics (Birkhäuser, Boston, 1996).
9. R. CHARNEY, 'Artin groups of finite type are biautomatic', Math. Ann. 292 (1992) 671-683.
10. R. CHARNEV, 'Geodesic automation and growth functions for Artin groups of finite type', Math. Ann. 301 (1995) 307-324.
11. A. H. CLIFFORD and G. B. PRESTON, The algebraic theory of semigroups, Mathematical Surveys and Monographs 7 (American Mathematical Society, Providence, RI, 1961).
12. P. DEHORNOY, 'Deux propriétés des groupes de tresses', C. R. Acad. Sci. Paris 315 (1992) 633-638.
13. P. DEHORNOY, 'Braid groups and left distributive operations', Trans. Amer. Math. Soc. 345 (1994) 115-151.
14. P. DEHORNOY, 'The structure group for the associating identity', J. Pure Appl. Algebra 111 (1996) 59-82.
15. P. DEHORNOY, 'Groups with a complemented presentation', J. Pure Appl. Algebra 116 (1997) 115-137.
16. P. DELIGNE, 'Les immeubles des groupes de tresses généralisés', Invent. Math. 17 (1972) 273-302.
17. E. A. ELRIFAI and H. R. MORTON, 'Algorithms for positive braids', Quart. J. Math. Oxford Ser. (2) 45 (1994) 479-497.
18. D. B. A. EPSTEIN et al., Word processing in groups (Jones and Bartlett, Boston, 1992).
19. F. A. GARSIDE, 'The braid group and other groups', Quart. J. Math. Oxford Ser. (2) 20 (1969) 235-254.
20. J. E. HUMPHREYS, Introduction to Lie algebras and representation theory (Springer, New York, 1972).
21. J. E. HUMPHREYS, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29 (Cambridge University Press, 1990).
22. C. LABRUÈRE, 'Groupes d'Artin et mapping class groups', PhD Thesis, Université de Bourgogne, 1997.
23. L. PARIS, 'Parabolic subgroups of Artin groups', J. Algebra 196 (1997) 369-399.
24. ℓ, J. Algebra 196 (1997) 400-435.
25. R. RANDELL, 'The fundamental group of the complement of a union of complex hyperplanes', Invent. Math. 69 (1982) 103-108;
26. correction, Invent. Math. 80 (1985) 467-468.
27. J. H. REMMERS, 'On the geometry of semigroup presentations', Adv. in Math. 36 (1980) 283-296.
28. D. ROLFSEN, Knots and links, Mathematics Lecture Series 7 (Publish or Perish, Houston, 1976).
29. N', Invent. Math. 88 (1987) 603-618.
30. K. TATSUOKA, 'An isoperimetric inequality for Artin groups of finite type', Trans. Amer. Math. Soc. 339 (1993) 537-551.
31. J. TITS, 'Le problème des mots dans les groupes de Coxeter', Symposia Mathematica (INDAM, Rome, 1967-68) (Academic Press, London, 1969) 175-185.
32. H. VAN DER LEK, 'The homotopy type of complex hyperplane complements', PhD Thesis, Nijmegen, 1983.