Twisted quantum doubles.
Fukuda, Daijiro, Kuga, Ken'ichi (2004)
International Journal of Mathematics and Mathematical Sciences
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Fukuda, Daijiro, Kuga, Ken'ichi (2004)
International Journal of Mathematics and Mathematical Sciences
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Stanisław Zakrzewski (1997)
Banach Center Publications
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We show that a Poisson Lie group (G,π) is coboundary if and only if the natural action of G×G on M=G is a Poisson action for an appropriate Poisson structure on M (the structure turns out to be the well known ). We analyze the same condition in the context of Hopf algebras. A quantum analogue of the structure on SU(N) is described in terms of generators and relations as an example.
J. Donin, D. Gurevich, S. Majid (1993)
Annales de l'I.H.P. Physique théorique
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Michael Semenov-Tian-Shansky (1993-1994)
Séminaire Bourbaki
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Ionescu, Lucian M., Marsalli, Michael (2008)
APPS. Applied Sciences
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A. A. Balinsky (2000)
Commentationes Mathematicae Universitatis Carolinae
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A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.