Casimirs and Lax Operators from the Structure of Lie algebras

Authors

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

Keywords:

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

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.

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

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Published

2012-11-07

Issue

Vol. 5 No. 4: (October 2012)

Section

Functional Analysis

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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. https://www.ejpam.com/index.php/ejpam/article/view/1515