Casimirs and Lax operators from the structure of Lie algebras

Linton, C., Holderbaum, W. ORCID: https://orcid.org/0000-0002-1677-9624 and Biggs, J. (2012) Casimirs and Lax operators from the structure of Lie algebras. European Journal of Pure and Applied Mathematics, 5 (4). pp. 567-583. ISSN 1307-5543

Abstract/Summary

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.