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.
Funding
This research has been partially supported by Ministerio de Economía, Industria y Competitividad (MINECO), Agencia Estatal de Investigación (AEI), and European Regional Development Fund (ERDF, EU), through project COPCIS, grant number TIN2017-84844-C2-1-R, and by Comunidad de Madrid (Spain) through project CYNAMON, grant number P2018/TCS-4566-CM, co-funded along with ERDF.
