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On moment maps associated to a twisted Heisenberg double

Ctirad Klimcik
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Abstract

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 $(D,κ)$ 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 $(D,κ)$. The absence of the anomaly of this "quasi-adjoint" moment map permits to perform the gauging of deformed WZW models.

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Ctirad Klimcik. 2006-10-30. On moment maps associated to a twisted Heisenberg double. https://doi.org/10.1142/s0129055x06002796

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