Abstract:
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, № 3, P. 476–519), where the history of the problem is covered, and a list of references provided.
Bibliography: 2 titles.