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This paper develops the technique of constructing Lax representations forPDEs via non-central extensions generated by non-triivial exotic 2-cocycles oftheir contact symmetry algebras. We show that the method is applicable to theLax representations with non-removable spectral parameters. Also we demonstratethat natural extensions of the symmetry algebras produce the integrablehierarchies associated to their PDEs.

Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras