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.
- is a vector space
- is the multiplication map
- is the co-product map
- is the unit operator
- is the co-unit operator
- is the antipode
- is a universal R matrix
We assume that the underlying field is
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