On moment maps associated to a twisted Heisenberg double

Details On moment maps associated to a twisted Heisenberg double On moment maps associated to a twisted Heisenberg double

2006-02-20

arxiv.org/abs/math-ph/0602048v2

Rev.Math.Phys.18:781-821,2006

Physics

Mathematical Physics

52 pages, LaTeX, introduction substantially enlarged, several explanatory remarks added, final published version

Scientific paper

10.1142/S0129055X06002796

We review the concept of the (anomalous) Poisson-Lie symmetry in a way that emphasises the notion of Poisson-Lie Hamiltonian. The language that we develop turns out to be very useful for several applications: we prove that the left and the right actions of a group $G$ on its twisted Heisenberg double $(D,\kappa)$ realize the (anomalous) Poisson-Lie symmetries and we explain in a very transparent way the concept of the Poisson-Lie subsymmetry and that of Poisson-Lie symplectic reduction. Under some additional conditions, we construct also a non-anomalous moment map corresponding to a sort of quasi-adjoint action of $G$ on $(D,\kappa)$. The absence of the anomaly of this "quasi-adjoint" moment map permits to perform the gauging of deformed WZW models.

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