Symmetry algebras of Lagrangian Liouville-type systems

TL;DR

This paper explicitly computes the generators and commutation relations of higher symmetry algebras for a class of hyperbolic Euler-Lagrange systems of Liouville type, including 2D Toda chains linked to semi-simple Lie algebras.

Contribution

It provides explicit calculations of symmetry algebra generators and their relations for Liouville-type systems, advancing understanding of their algebraic structures.

Findings

Explicit symmetry generators for Liouville-type systems

Commutation relations for higher symmetry algebras

Application to 2D Toda chains and Lie algebras

Abstract

The generators and commutation relations are calculated explicitly for higher symmetry algebras of a class of hyperbolic Euler-Lagrange systems of Liouville type (in particular, for 2D Toda chains associated with semi-simple complex Lie algebras). Mathematics Subject Classification (2000): 35Q53, 37K05, 37K30.