Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations.
The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The use of the exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDEs under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.
Publisher URL: http://arxiv.org/abs/1706.01090
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