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WZW-Poisson manifolds. (English) Zbl 1027.70023

Summary: We observe that a term of WZW-type can be added to the Lagrangian of Poisson \(\sigma\)-model in such a way that the algebra of first-class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting WZW-Poisson manifold \(M\) is characterized by a bivector \(\Pi\) and by a closed three-form \(H\) such that \(1/2[\Pi,\Pi]_S= \langle H,\pi \otimes \Pi \otimes \Pi \rangle\), the symbol \([\cdot,\cdot]_S\) denotes the Schouten bracket.

MSC:

70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
53D17 Poisson manifolds; Poisson groupoids and algebroids

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