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
- Altschuler, D.; Coste, A. (1992). "Quasi-quantum groups, knots, three-manifolds and topological field theory". Commun. Math. Phys. 150: 83–107. arXiv:hep-th/9202047. doi:10.1007/bf02096567.
- Chari, V. C.; Pressley, A. (1994). A Guide to Quantum Groups. Cambridge University Press. ISBN 0-521-55884-0.
- Drinfeld, Vladimir (1989). "Quasi-Hopf algebras". Leningrad Math J. 1: 1419–1457.
- Majid, Shahn (1995). Foundations of Quantum Group Theory. Cambridge University Press.
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