In mathematics, the braid group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are...

spherical braid group or Hurwitz braid group is a braid group on n strands. In comparison with the usual braid group, it has an additional group relation...

range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The structure is usually long and...

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...

theoretical physics, braid statistics is a generalization of the spin statistics of bosons and fermions based on the concept of braid group. While for fermions...

center; equivalently, to the group of inner automorphisms of B3. The braid group B3 in turn is isomorphic to the knot group of the trefoil knot. The quotients...

the classifying space of the n {\displaystyle n} th braid group (see below). The n-strand braid group on a connected topological space X is B n ( X ) :=...

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...

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...

mostly to cryptographic protocols that use infinite non-abelian groups such as a braid group. Shpilrain–Zapata public-key protocols Magyarik–Wagner public...

A generalized braid group is said to be of spherical type if the associated Coxeter group is finite. If B is a generalized braid group of spherical type...

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...

Yang–Baxter equation also shows up when discussing knot theory and the braid groups where R {\displaystyle R} corresponds to swapping two strands. Since...

Braid is an American emo band from Champaign, Illinois, formed in 1993. Following several early line-up changes, the band eventually settled on Bob Nanna...

range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The structure is usually long and...

SkyTrain station Braid, a civil parish in County Antrim, Northern Ireland Braid in Edinburgh: Hermitage of Braid Braid Hills Braid Burn Braid theory, an abstract...

term group-based cryptography refers mostly to cryptographic protocols that use infinite non-abelian groups such as a braid group. List of group theory...

symmetric group over an arbitrary field is widely regarded as one of the most important open problems in representation theory. Braid group History of group theory...

is the trace closure of a braid, say with n strands. Now define a representation ρ {\displaystyle \rho } of the braid group on n strands, Bn, into the...

identities defined below. The term braided references the fact that the braid group plays an important role in the theory of braided monoidal categories. Partly...

James Braid (19 June 1795 – 25 March 1860) was a Scottish surgeon, natural philosopher, and "gentleman scientist". He was a significant innovator in the...

A braid algebra can be: A Gerstenhaber algebra (also called an antibracket algebra). An algebra related to the braid group. This disambiguation page lists...

group of the trefoil knot is known to be the braid group B 3 , {\displaystyle B_{3},} which gives another example of a non-abelian fundamental group....

around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions). These braids form the logic gates that...

{\displaystyle \langle x,y\mid xyx=yxy\rangle .} This group is isomorphic to the braid group with three strands. As the simplest nontrivial knot, the...

third relation are sometimes called the braid relations.) When n = 2 {\displaystyle n=2} , the affine symmetric group S ~ 2 {\displaystyle {\widetilde {S}}_{2}}...

Coxeter group. Matsumoto's theorem implies that there is a natural map (not a group homomorphism) from a Coxeter group to the corresponding braid group, taking...

introduced, among other things, certain novel linear representations of the braid group — known as Lawrence–Krammer representations. In papers published in 2000...

increases, the number of crossing patterns increases, as described by the braid group. Various visual effects are also possible by shifting the center lines...

denominator closure Tangle numerator closure Reciprocal tangle Braid theory Braid group Band sum Flype Fox n-coloring Tricolorability Knot sum Reidemeister...