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Trigonometric dynamical r-matrices over Poisson Lie base

A. Mudrov
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Abstract

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

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A. Mudrov. 2004-03-12. Trigonometric dynamical r-matrices over Poisson Lie base. https://doi.org/10.1007/s11005-004-5924-5

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