Square-Zero Basis of Matrix Lie Algebras
R. Dur\'an D\'iaz, V. Gayoso Mart\'inez, L. Hern\'andez Encinas, J., Mu\~noz Masqu\'e
TL;DR
This paper introduces a method to determine the maximum number of independent invariant functions for certain Lie algebras, specifically those with a basis of square-zero matrices, with some applications demonstrated.
Contribution
It provides a novel approach to compute invariants for Lie algebras with square-zero bases, expanding understanding of their structure and symmetries.
Findings
Method to compute maximum invariant functions for Lie algebras with square-zero bases
Application examples demonstrating the method's utility
Enhanced understanding of invariants in algebraic group actions
Abstract
A method is obtained 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 base of square-zero matrices. Some applications are also given.
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