dorsal/arxiv
View SchemaBihamiltonian Reductions and W_n Algebras
| Authors | Paolo Casati, Gregorio Falqui, Franco Magri, Marco Pedroni |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9707017 |
| URL | https://arxiv.org/abs/solv-int/9707017 |
| DOI | 10.1016/S0393-0440(97)00060-0 |
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.
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"abstract": "We discuss the geometry of the Marsden-Ratiu reduction theorem for a\nbihamiltonian manifold. We consider the case of the manifolds associated with\nthe Gel\u0027fand-Dickey theory, i.e., loop algebras over sl(n+1). We provide an\nexplicit identification, tailored on the MR reduction, of the\nAdler-Gel\u0027fand-Dickey brackets with the Poisson brackets on the MR-reduced\nbihamiltonian manifold N. Such an identification relies on a suitable immersion\nof the space of sections of the cotangent bundle of N into the algebra of\npseudo differential operators connected to geometrical features of the theory\nof (classical) W_n algebras.",
"arxiv_id": "solv-int/9707017",
"authors": [
"Paolo Casati",
"Gregorio Falqui",
"Franco Magri",
"Marco Pedroni"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/S0393-0440(97)00060-0",
"title": "Bihamiltonian Reductions and W_n Algebras",
"url": "https://arxiv.org/abs/solv-int/9707017"
},
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