The Square-Zero Basis of Matrix Lie Algebras

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 algebra...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-06, Vol.8 (6), p.1032
Main Authors: Durán Díaz, Raúl, Gayoso Martínez, Víctor, Hernández Encinas, Luis, Muñoz Masqué, Jaime
Format: Article
Language:English
Subjects:
invariant function
Lie algebra of matrices
linear algebraic groups
linear representation
square-zero matrix
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8061032