In mathematics, a braided vectorspace
such that the Yang–Baxter equation is fulfilled. Hence drawing tensor diagrams with
As first example, every vector space is braided via the trivial braiding (simply flipping). A superspace has a braiding with negative sign in braiding two odd vectors. More generally, a diagonal braiding means that for a
A good source for braided vector spaces entire braided monoidal categories with braidings between any objects
If
Examples of such braided algebras (and even Hopf algebras) are the Nichols algebras, that are by definition generated by a given braided vectorspace. They appear as quantum Borel part of quantum groups and often (e.g. when finite or over an abelian group) possess an arithmetic root system, multiple Dynkin diagrams and a PBW-basis made up of braided commutators just like the ones in semisimple Lie algebras.