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

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

See also

References

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