The Square-Zero Basis of Matrix Lie Algebras

R. Durán Díaz, V. Gayoso Martínez, L. Hernández Encinas and J. Muñoz Masqué
Mathematics, 8(6), 1032 (2020), 9 pp., Special Issue “Algebra and Its Applications” (Q1, Mathematics, F.I. 1.747)

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.