Dressing operator approach to Moyal algebraic deformation of selfdual gravity

Details Dressing operator approach to Moyal algebraic deformation of selfdual gravity Dressing operator approach to Moyal algebraic deformation of selfdual gravity

1992-12-17

arxiv.org/abs/hep-th/9212103v1

J. Geom. Phys. 14 (1994) 111-120

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Kyoto University KUCP-0054/92

Scientific paper

Recently Strachan introduced a Moyal algebraic deformation of selfdual gravity, replacing a Poisson bracket of the Plebanski equation by a Moyal bracket. The dressing operator method in soliton theory can be extended to this Moyal algebraic deformation of selfdual gravity. Dressing operators are defined as Laurent series with coefficients in the Moyal (or star product) algebra, and turn out to satisfy a factorization relation similar to the case of the KP and Toda hierarchies. It is a loop algebra of the Moyal algebra (i.e., of a $W_\infty$ algebra) and an associated loop group that characterize this factorization relation. The nonlinear problem is linearized on this loop group and turns out to be integrable.

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