English

Trigonometric dynamical r-matrices over Poisson Lie base

Quantum Algebra 2009-11-10 v1

Abstract

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

Keywords

Cite

@article{arxiv.math/0403207,
  title  = {Trigonometric dynamical r-matrices over Poisson Lie base},
  author = {A. Mudrov},
  journal= {arXiv preprint arXiv:math/0403207},
  year   = {2009}
}

Comments

AMS LaTeX, 8 pages