Bihamiltonian Reductions and W_n Algebras

Abstract

We discuss the geometry of the Marsden-Ratiu reduction theorem for a bihamiltonian manifold. We consider the case of the manifolds associated with the Gel'fand-Dickey theory, i.e., loop algebras over sl(n+1). We provide an explicit identification, tailored on the MR reduction, of the Adler-Gel'fand-Dickey brackets with the Poisson brackets on the MR-reduced bihamiltonian manifold N. Such an identification relies on a suitable immersion of the space of sections of the cotangent bundle of N into the algebra of pseudo differential operators connected to geometrical features of the theory of (classical) W_n algebras.

LaTeX2e, 23 pages, to be published in J. Geom. Phys

References in corpus (1)

• The Algebra of Differential Operators on the Circle and $W_{KP}^{(q)}$

Cited by in corpus (4)

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• On classification and construction of algebraic Frobenius manifolds
• Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation
• Poisson pencils: reduction, exactness, and invariants