On matrix differential equations and abstract FG algorithm (Q1602998)

The purpose of this paper is to show that a whole class of matrix differential equations has a connection with the abstract FG algorithm. All equations from this class are built by means of various representations \(\rho\) of an arbitrary Lie algebra \({\mathfrak g}\) on \(\mathbb{K}^{n\times n}\) in the following way: \[ \dot L=\rho_N(L) \] where \(L\in\mathbb{K}^{n\times n}\), and \(N=N(t,L)\in{\mathfrak g}\). Here the author assumes that \({\mathfrak g}\) is the Lie algebra of a certain closed subgroup \({\mathfrak h}\) of \(GL(n,\mathbb{K})\).