In mathematics, a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfeld...

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)...

Artin–Tits group Braided monoidal category Braided vector space Braided Hopf algebra Knot theory Non-commutative cryptography Spherical braid group Weisstein...

compared to before. Braided vector space Braided Hopf algebra Monoidal category Multilinear algebra Fock space Bourbaki, Nicolas (1989). Algebra I. Chapters 1-3...

In algebra, the Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted...

type of braided monoidal category. It consists of modules over a Hopf algebra which satisfy some additional axioms. Let H be a Hopf algebra over a field...

double construction. If the Hopf algebra H is quasitriangular, then the category of modules over H is braided with braiding c U , V ( u ⊗ v ) = T ( R ⋅...

noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix...

Nichols algebra is a Hopf algebra in a braided category assigned to an object V in this category (e.g. a braided vector space). The Nichols algebra is a...

Examples of such braided algebras (and even Hopf algebras) are the Nichols algebras, that are by definition generated by a given braided vectorspace. They...

Society. In the 1990s, Majid introduced the theory of braided groups or braided Hopf algebras as the true objects underlying q {\displaystyle q} -deformations...

instance, adding a quasitriangular structure to the weak Hopf algebra corresponds to adding a braiding on the representation category. In their original work...

momentum on it expressed as the structure of a braided Hopf algebra or quantum group in a certain braided monoidal category). This theory, by 1993, had...

a Lie algebra Frobenius integrability theorem (the integrability being the same as being a Lie subalgebra) Gelfand–Fuks cohomology Hopf algebra Index...

"standard" braid corresponding to the Borromean rings gives rise to the Hopf fibration S3 → S2, and iteration of this (as in everyday braiding) is likewise...

Hopf link is ±1. The Hopf link is a (2,2)-torus link with the braid word σ 1 2 . {\displaystyle \sigma _{1}^{2}.\,} The knot complement of the Hopf link...

theorem to hold). Just as for Lie algebras, the universal enveloping algebra of the Lie superalgebra can be given a Hopf algebra structure. Lie superalgebras...

category A − M o d {\displaystyle {\mathcal {A}}-Mod} is braided. Equivalently, by analogy with braided bialgebras, we can construct a notion of a universal...

^{0},\hbar } ). Lie bialgebra Yangian Reidemeister move Quasitriangular Hopf algebra Yang–Baxter operator H.-D. Doebner, J.-D. Hennig, eds, Quantum groups...

of Sn, computed by the algebraic sum of their points, corresponding to the degree of maps f : Sn → Sn. The projection of the Hopf fibration S3 → S2 represents...

nontrivial example of a link with more than one component is called the Hopf link, which consists of two circles (or unknots) linked together once. The...

Birkhoff, G. (1999). Algebra. AMS Chelsea. ISBN 0-8218-1646-2. Aguiar, M.; Mahajan, S. (2010). Monoidal functors, species and Hopf algebras. CRM Monograph Series...

Brunnian link, a set of links which become trivial if one loop is removed Hopf link, the simplest non-trivial link Solomon's knot, a two-ring link with...

abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper. As in algebraic topology...

crossings (the Hopf link [1]). Patching the trefoil P() = A × P() + P() gives the unknot and, again, the Hopf link. Patching the Hopf link P() = A × P()...

different examples of braided monoidal categories were found in rational conformal field theory. Tannaka–Krein philosophy suggests that braided monoidal categories...

enveloping algebras, it has a natural structure of a Hopf algebra, with a coproduct Δ. The ring S used above is just a completion of this Hopf algebra. A related...

study of operator algebras. In Jones' approach, it resulted from a kind of "trace" of a particular braid representation into an algebra which originally...

sum of Jacobi diagrams (which carry a Lie algebra structure), and a representation of a ribbon Hopf algebra such as a quantum group. It is not clear a-priori...

This latter pentagonal symmetry of the 600-cell is captured by the set of Hopf coordinates (𝜉i, 𝜂, 𝜉j) given as: ({<10}⁠𝜋/5⁠, {≤5}⁠𝜋/10⁠, {<10}⁠𝜋/5⁠)...