Higher Dimensional Classical W-Algebras

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.

22 pages, Plain TeX, KUL-TF-92/19, US-FT/6-92

References in corpus (1)

• SDiff(2) KP hierarchy

Cited by in corpus (6)

• The Moyal bracket and the dispersionless limit of the KP hierarchy
• The Constrained KP Hierarchy and the Generalised Miura Transformation
• Generalized W(infinity) Higher-Spin Algebras and Symbolic Calculus on Flag Manifolds
• Chern-Simons $p$-Branes and $p$-Dimensional Classical $W$-Algebras
• Gauging of Chern-Simons $p$-branes
• Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya Equations