Casimirs and Lax Operators from the Structure of Lie algebras


  • Carol Linton University of Reading, UK
  • William Holderbaum University of Reading, Reading.
  • James Biggs University of Strathclyde


Casimir invariants, Lax operators, structure constants, matrix Lie algebras, Poisson manifolds


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.

Author Biographies

  • Carol Linton, University of Reading, UK

    School of Systems Engineering, Post graduate student

  • William Holderbaum, University of Reading, Reading.

    Senior Lecturer

    School of Systems Engineering

  • James Biggs, University of Strathclyde
    Associate Director of the Advanced Space Concepts Laboratory Department of Mechanical & Aerospace Engineering






Functional Analysis

How to Cite

Casimirs and Lax Operators from the Structure of Lie algebras. (2012). European Journal of Pure and Applied Mathematics, 5(4), 567-583.