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The Square-Zero Basis of Matrix Lie Algebras

Author

Listed:
  • Raúl Durán Díaz

    (Departamento de Automática, Universidad de Alcalá, E-28871 Alcalá de Henares, Spain)

  • Víctor Gayoso Martínez

    (Instituto de Tecnologías Físicas y de la Información (ITEFI) Consejo Superior de Investigaciones Científicas (CSIC), E-28006 Madrid, Spain)

  • Luis Hernández Encinas

    (Instituto de Tecnologías Físicas y de la Información (ITEFI) Consejo Superior de Investigaciones Científicas (CSIC), E-28006 Madrid, Spain)

  • Jaime Muñoz Masqué

    (Instituto de Tecnologías Físicas y de la Información (ITEFI) Consejo Superior de Investigaciones Científicas (CSIC), E-28006 Madrid, Spain)

Abstract

A method is presented that allows one to compute the maximum number of functionally-independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a basis of square-zero matrices even on a field of positive characteristic. The class of such Lie algebras is studied in the framework of the classical Lie algebras of arbitrary characteristic. Some examples and applications are also given.

Suggested Citation

  • Raúl Durán Díaz & Víctor Gayoso Martínez & Luis Hernández Encinas & Jaime Muñoz Masqué, 2020. "The Square-Zero Basis of Matrix Lie Algebras," Mathematics, MDPI, vol. 8(6), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1032-:d:375662
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