# Category: Braid groups

Double affine braid group
In mathematics, a double affine braid group is a group containing the braid group of an affine Weyl group. Their group rings have quotients called double affine Hecke algebras in the same way that the
Lawrence–Krammer representation
In mathematics the Lawrence–Krammer representation is a representation of the braid groups. It fits into a family of representations called the Lawrence representations. The first Lawrence representat
Affine braid group
In mathematics, an affine braid group is a braid group associated to an affine Coxeter system. Their group rings have quotients called affine Hecke algebras. They are subgroups of double affine braid
Burau representation
In mathematics the Burau representation is a representation of the braid groups, named after and originally studied by the German mathematician Werner Burau during the 1930s. The Burau representation
Braid group
In mathematics, the braid group on n strands (denoted ), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose gr
Dehornoy order
In the mathematical area of braid theory, the Dehornoy order is a left-invariant total order on the braid group, found by Patrick Dehornoy. Dehornoy's original discovery of the order on the braid grou
Group-based cryptography
Group-based cryptography is a use of groups to construct cryptographic primitives. A group is a very general algebraic object and most cryptographic schemes use groups in some way. In particular Diffi
Matsumoto's theorem (group theory)
In group theory, Matsumoto's theorem, proved by Hideya Matsumoto, gives conditions for two reduced words of a Coxeter group to represent the same element.
Braid theory
No description available.
Loop braid group
The loop braid group is a mathematical group structure that is used in some models of theoretical physics to model the exchange of particles with loop-like topologies within three dimensions of space
Braids, Links, and Mapping Class Groups
Braids, Links, and Mapping Class Groups is a mathematical monograph on braid groups and their applications in low-dimensional topology. It was written by Joan Birman, based on lecture notes by James W
Artin–Tits group
In the mathematical area of group theory, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete groups defined by simple presentations. They are