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Higher Dimensional Classical W-Algebras

Fernando Martinez-Moras·Eduardo Ramos
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Abstract

Classical $W$-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. These $W$-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 Diff$S(1)$ is taken by the algebra of generators of local diffeomorphisms in two dimensions.

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Fernando Martinez-Moras, Eduardo Ramos. 1992-06-09. Higher Dimensional Classical W-Algebras. https://doi.org/10.1007/bf02096883

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