Ribbon Hopf algebra
A ribbon Hopf algebra is a quasitriangular Hopf algebra which possess an invertible central element more commonly known as the ribbon element, such that the following conditions hold:
where. Note that the element u exists for any quasitriangular Hopf algebra, and
must always be central and satisfies, so that all that is required is that it have a central square root with the above properties.
Here
We assume that the underlying field is
If is finite-dimensional, one could equivalently call it ribbon Hopf if and only if its category of modules is ribbon; if is finite-dimensional and quasi-triangular, then it is ribbon if and only if its category of modules is pivotal.
