Geodesic
Systems of generators for centralizers of rigid elements of the braid group
Izvestiya. Mathematics, Tome 31 (1988) no. 2, pp. 223-244 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of describing centralizers of elements of the braid group was posed by Artin in 1947. An element of the braid group $\mathfrak B_{n+1}$ is said to be rigid if it can be represented as a positive word that is not equal to any other word in the braid semigroup. Explicit expressions are given for finite systems of generators for the centralizers of a wide class of rigid elements. The article is a continuation of the author's paper Systems of generators for the normalizers of certain elements of the braid group (Izv. Akad. Nauk SSSR. Ser. Mat., 1984, V. 48, No 3, P. 476–519), where the history of the problem is covered, and a list of references provided. Bibliography: 2 titles. 
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     title = {Systems of generators for centralizers of rigid elements of the braid group},
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G. G. Gurzo. Systems of generators for centralizers of rigid elements of the braid group. Izvestiya. Mathematics, Tome 31 (1988) no. 2, pp. 223-244. http://geodesic.mathdoc.fr/item/IM2_1988_31_2_a0/

[1] Gurzo G. G., “Sistemy obrazuyuschikh dlya normalizatorov nekotorykh elementov gruppy kos”, Izv. AN SSSR. Ser. matem., 48:3 (1984), 476–519 | MR | Zbl

[2] Artin E., “Theory of Braids”, Ann. Math., 48 (1947), 101–126 | DOI | MR | Zbl