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...

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

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

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...

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

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...

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...

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

Gelfand–Fuks cohomology Hopf algebra Index of a Lie algebra Leibniz algebra Lie algebra cohomology Lie algebra extension Lie algebra representation Lie bialgebra...

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...

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

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...

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...

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...

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...

^{0},\hbar } ). Lie bialgebra Yangian Reidemeister move Quasitriangular Hopf algebra H.-D. Doebner, J.-D. Hennig, eds, Quantum groups, Proceedings of the...

"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...

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...

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...

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()...

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...

(1770) Also known as Elements of Algebra, Euler's textbook on elementary algebra is one of the first to set out algebra in the modern form we would recognize...

While mainly used to obtain invariants of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle...

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

Hua-Lin; Liu, Gongxiang; Ye, Yu (2014). "The braided monoidal structures on a class of linear Gr-categories". Algebras and Representation Theory. 17 (4): 1249–1265...

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...

quantum gravity spin network black hole thermodynamics Quantum group Hopf algebra Noncommutative quantum field theory See list of string theory topics...

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...

(1988). "Geometry of the Hopf Mapping and Pinkall's Tori of Given Conformal Type". In Tangora, Martin (ed.). Computers in Algebra. New York and Basel: Marcel...