Higher dimensional classicalW-algebras |
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Authors: | Fernando Martinez-Moras Eduardo Ramos |
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Affiliation: | (1) Departamento de Física de Partículas Elementales, Universidad de Santiago, 15706 Santiago de Compostela, Spain;(2) Department of Physics, Queen Mary and Westfield College, Mile End Road, E1 4NS London, UK |
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Abstract: | ClassicalW-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. TheseW-algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). The two dimensional case is worked out explicitly and it is shown that the role of DiffS(1) is taken by the algebra of generators of local diffeomorphisms in two dimensions. |
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