Nonabelian KP hierarchy with Moyal algebraic coefficients

Abstract

A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-$N$ limit of multi-component ($\gl(N)$ symmetric) KP hierarchies. Actually, two different hierarchies are constructed. The first hierarchy consists of commuting flows and may be thought of as a straightforward extension of the ordinary and multi-component KP hierarchies. The second one is a hierarchy of noncommuting flows, and related to Moyal algebraic deformations of selfdual gravity. Both hierarchies turn out to possess quasi-classical limit, replacing Moyal algebraic structures by Poisson algebraic structures. The language of W-infinity algebras provides a unified point of view to these results.

37 pages, Kyoto University KUCP-0062/93

References in corpus (2)

• SDiff(2) Toda equation -- hierarchy, $\tau$ function, and symmetries
• Dressing operator approach to Moyal algebraic deformation of selfdual gravity

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