Geodesic
Orders on Braid Groups
Algebra i logika, Tome 42 (2003) no. 3, pp. 312-319.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the braid group $B(n)$ $(n\geqslant 3)$ defies lattice ordering.
Keywords: braid group, lattice-ordered group ($l$-group), right linear order. 
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N. Ya. Medvedev. Orders on Braid Groups. Algebra i logika, Tome 42 (2003) no. 3, pp. 312-319. http://geodesic.mathdoc.fr/item/AL_2003_42_3_a3/

[1] E. Artin, “Theorie der Zöpfe”, Abn. Math. Sem. Univ. Hamburg, 4:1 (1925), 47–72 | DOI | Zbl

[2] P. Dehornoy, “From large cardinals to braids via distributive algebra”, J. Knot Theory Ramifications, 4:1 (1995), 33–79 | DOI | MR | Zbl

[3] V. M. Kopytov, Reshetochno uporyadochennye gruppy, Nauka, M., 1984 | MR | Zbl

[4] V. M. Kopytov, N. Ya. Medvedev, Pravouporyadochennye gruppy, Sibirskaya shkola algebry i logiki, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1996 | MR | Zbl

[5] M. I. Kargapolov, Yu. I. Merzlyakov, Teoriya grupp, Nauka, M., 1977 | MR | Zbl

[6] E. A. Gorin, V. Ya. Lin, “Algebraicheskie uravneniya s nepreryvnymi koeffitsientami i nekotorye voprosy algebraicheskoi teorii kos”, Matem. sb., 78(120):4 (1969), 579–610 | MR | Zbl

[7] Wei-Liang Chow, “On the algebraical braid group”, Ann. Math., 49:3 (1948), 654–658 | DOI | MR | Zbl

[8] A. A. Markov, “Osnovy algebraicheskoi teorii kos”, Trudy matem. in-ta AN SSSR, 16 (1945), 3–53 | MR | Zbl

[9] T. V. Dubrovina, N. I. Dubrovin, “O gruppakh kos”, Matem. sb., 192:5 (2001), 53–64 | MR