# Lax representations with non-removable parameter and exotic cohomology of symmetry algebras of PDEs

## TL;DR

This paper introduces a method to construct Lax representations with non-removable spectral parameters for PDEs using non-central extensions of their contact symmetry algebras, advancing the understanding of integrability structures.

## Contribution

It develops a novel technique for deriving Lax representations with non-removable parameters through non-central extensions of symmetry algebras.

## Key findings

- Applicable to PDEs with contact symmetry algebras
- Enables construction of Lax pairs with non-removable spectral parameters
- Provides new insights into the cohomology of symmetry algebras

## Abstract

This paper develops the technique of constructing Lax representations for PDEs via non-central extensions of their contact symmetry algebras. We show that the method is applicable to the Lax representations with non-removable spectral parameters.