PoissonLie Tduality for quasitriangular Lie bialgebras
Abstract
We introduce a new 2parameter family of sigma models exhibiting PoissonLie Tduality on a quasitriangular PoissonLie group $G$. The models contain previously known models as well as a new 1parameter line of models having the novel feature that the Lagrangian takes the simple form $L=E(u^{1}u_+,u^{1}u_)$ where the generalised metric $E$ is constant (not dependent on the field $u$ as in previous models). We characterise these models in terms of a global conserved $G$invariance. The models on $G=SU_2$ and its dual $G^\star$ are computed explicitly. The general theory of PoissonLie Tduality is also extended; we develop the Hamiltonian formulation and the reduction for constant loops to integrable motion on the group manifold. Finally, we generalise Tduality in the Hamiltonian formulation to group factorisations $D=G\dcross M$ where the subgroups need not be dual or even have the same dimension and need not be connected to the Drinfeld double or to Poisson structures.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:math/9906040
 Bibcode:
 1999math......6040B
 Keywords:

 Quantum Algebra
 EPrint:
 42 pages Latex, no figures