Casimirs and Lax operators from the structure of Lie algebras

Abstract

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. 2010 Mathematics Subject Classifications: 17B45, 53D17, 17B63