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WZW–Poisson manifolds

✍ Scribed by C. Klimčı́k; T. Strobl

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
44 KB
Volume
43
Category
Article
ISSN
0393-0440

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✦ Synopsis

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ -model in such a way that the algebra of the 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 Π and by a closed three-form H such that 1/2[Π, Π] Schouten = H, Π ⊗ Π ⊗ Π .

📜 SIMILAR VOLUMES

Reduction of Poisson manifolds
Reduction of Poisson manifolds
✍ Jerrold E. Marsden; Tudor Ratiu 📂 Article 📅 1986 🏛 Springer 🌐 English ⚖ 447 KB

Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as results such as the Dirac bracket and the reduction to the Lie-Poisson bracket.