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

## TL;DR

This paper introduces a novel method for constructing Lax representations with non-removable spectral parameters for PDEs using exotic cohomology of symmetry algebras, leading to integrable hierarchies.

## Contribution

It develops a new technique leveraging exotic cohomology to generate Lax representations with non-removable parameters and associated integrable hierarchies.

## Key findings

- Method applicable to PDEs with non-removable spectral parameters
- Constructs Lax representations via exotic 2-cocycles
- Produces integrable hierarchies from symmetry algebra extensions

## Abstract

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