SDiff(2) and uniqueness of the Plebański equation

Details SDiff(2) and uniqueness of the Plebański equation SDiff(2) and uniqueness of the Plebański equation

2012-04-16

arxiv.org/abs/1204.3577v2

Physics

Mathematical Physics

Scientific paper

The group of area preserving diffeomorphisms showed importance in the problems of self-dual gravity and integrability theory. We discuss how representations of this infinite-dimensional Lie group can arise in mathematical physics from pure local considerations. Then using Lie algebra extensions and cohomology we derive the second Pleba\'{n}ski equation and its geometry. We do not use K\"ahler or other additional structures but obtain the equation solely from the geometry of area preserving transformations group. We conclude that the Pleba\'{n}ski equation is Lie remarkable.

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