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| Twisting | |
| 2>
The property of being a quasi-triangular Hopf algebra is preserved by twisting via an invertible element such that and satisfying the cocycle condition
Furthermore,
u =
∑
fiS(fi)
i
is invertible and the twisted antipode is given by S'(a) = uS(a)u − 1, with the twisted comultiplication, R-matrix and co-unit change according to those defined for the quasi-triangular Quasi-Hopf algebra. Such a twist is known as an admissible (or Drinfel'd) twist.
[edit] Tags:Hopf Algebra,Drinfel'd,Quasi-triangular Hopf Algebra,Quasi-triangular Quasi-hopf Algebra, | |
| References | |
| 2>
Susan Montgomery, Hans-Jürgen Schneider. New directions in Hopf algebras, Volume 43. Cambridge University Press, 2002. ISBN 9780521815123
Retrieved from "http://en.wikipedia.org/w/index.php?title=Quasitriangular_Hopf_algebra&oldid=473107403"
Categories: Hopf algebrasHidden categories: Articles needing additional references from December 2009All articles needing additional references
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