Ribbon Hopf algebra
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A Ribbon Hopf algebra 
is a Quasitriangular Hopf algebra which possess an invertible central element ν more commonly known as the ribbon element, such that the following conditions hold:
such that 
. Note that the element u exists for any quasitriangular Hopf algebra, and uS(u) 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
- A is a vector space
- m is the multiplication map
- Δ is the co-product map
- u is the unit operator
is the co-unit opertor 
is a universal R matrix
We assume that the underlying field K is 
[edit] See also
[edit] References
- Altschuler, D., Coste, A.: Quasi-quantum groups, knots, three-manifolds and topological field theory. Commun. Math. Phys. 150 1992 83-107 http://arxiv.org/pdf/hep-th/9202047
- Chari, V.C., Pressley, A.: A Guide to Quantum Groups Cambridge University Press, 1994 ISBN 0-521-55884-0.
- Vladimir Drinfeld, Quasi-Hopf algebras, Leningrad Math J. 1 (1989), 1419-1457
- Majid, S.: Foundations of Quantum Group Theory Cambridge University Press, 1995
