Deformations of infinite-dimensional Lie algebras, exotic cohomology and integrable nonlinear partial differential equations. II

Abstract: We consider the four-dimensional reduced quasi-classical self-dual Yang--Mills equation and show that non-triviality of the second exotic cohomology group of its symmetry algebra implies existence of a two-component integrable generalization of this equation. The sequence of natural extensions of this symmetry algebra generate an integrable hierarchy of multi-dimensional nonlinear PDEs. We write out the first three elements of this hierarchy.