Trigonometric dynamical r-matrices over Poisson Lie base

Details Trigonometric dynamical r-matrices over Poisson Lie base Trigonometric dynamical r-matrices over Poisson Lie base

2004-03-12

arxiv.org/abs/math/0403207v1

Mathematics

Quantum Algebra

AMS LaTeX, 8 pages

Scientific paper

10.1007/s11005-004-5924-5

Let $\g$ be a finite dimensional complex Lie algebra and $\l\subset \g$ a Lie subalgebra equipped with the structure of a factorizable quasitriangular Lie bialgebra. Consider the Lie group $\Exp \l$ with the Semenov-Tjan-Shansky Poisson bracket as a Poisson Lie manifold for the double Lie bialgebra $\D\l$. Let $\Nc_\l(0)\subset \l$ be an open domain parameterizing a neighborhood of the identity in $\Exp \l$ by the exponential map. We present dynamical $r$-matrices with values in $\g\wedge \g$ over the Poisson Lie base manifold $\Nc_\l(0)$.

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