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Quadratic brackets from symplectic forms

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arxiv hep-th/9307026 v1 pith:M5KLHRYJ submitted 1993-07-05 hep-th

Quadratic brackets from symplectic forms

classification hep-th
keywords quadraticactionsalgebrasappearbelievedbracetsbracketschiral
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is that quadratic Poisson bracets appear for group--like variables. It is believed that after quantization they lead to quadratic exchange algebras.

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