The Square-Zero Basis of Matrix Lie Algebras

Mathematics

Raúl Durán Díaz¹  Jaime Muñoz Masqué²  Víctor Gayoso Martínez²  Luis Hernández Encinas² 

[1] Departamento de Automática, Universidad de Alcalá, E-28871 Alcalá de Henares, Spain;Instituto de Tecnologías Físicas y de la Información (ITEFI) Consejo Superior de Investigaciones Científicas (CSIC), E-28006 Madrid, Spain;

关键词: invariant function;    Lie algebra of matrices;    linear algebraic groups;    linear representation;    square-zero matrix;   

DOI  :  10.3390/math8061032

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown