Remarks on Bihamiltonian Geometry and Classical $W$-algebras

Details Remarks on Bihamiltonian Geometry and Classical $W$-algebras Remarks on Bihamiltonian Geometry and Classical $W$-algebras

2009-11-11

arxiv.org/abs/0911.2116v2

Mathematics

Differential Geometry

revised for clarity

Scientific paper

We obtain the classical $W$-algebras associated to nilpotent orbits in a simple Lie algebra from the generalized bihamiltonian reduction. We prove that the bihamiltonian reduction leads naturally to the Dirac and the generalized Drinfeld-Sokolov reductions. This implies that the reduced structures depend only on the nilpotent orbit but not on the choice of a good grading or an isotropic subspace. We also clarify the relation with the finite $W$-algebras.

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