almost cocommutative bialgebra

A bialgebraPlanetmathPlanetmath A is called almost cocommutative if there is an unit AA such that


where Δop is the opposite comultiplication (the usual comultiplication, composed with the flip map of the tensor productPlanetmathPlanetmath AA). The element is often called the -matrix of A.

The significance of the almost cocommutative condition is that σV,W=σ:VWWV gives a natural isomorphism of bialgebra representations, where V and W are A-modules, making the categoryMathworldPlanetmath of A-modules into a quasi-tensor or braided monoidal category. Note that σW,VσV,W is not necessarily the identityPlanetmathPlanetmath (this is the braiding of the category).

Title almost cocommutative bialgebra
Canonical name AlmostCocommutativeBialgebra
Date of creation 2013-03-22 13:31:50
Last modified on 2013-03-22 13:31:50
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Definition
Classification msc 16W30