The Square-Zero Basis of Matrix Lie Algebras

Raúl Durán Díaz, Víctor Gayoso Martínez, Luis Hernández Encinas and Jaime Muñoz Masqué
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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

Mathematics, 2020, vol. 8, issue 6, 1-9

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.

Keywords: invariant function; Lie algebra of matrices; linear algebraic groups; linear representation; square-zero matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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