Models for free nilpotent Lie algebras
The free nilpotent Lie algebra \({\mathfrak g}_{M,r}\) is the quotient of the free Lie algebra \({\mathfrak g}_ M\) in M generators by the r-th element of the upper central series. The authors show how one can realize this Lie algebra by vector-fields on \({\mathbb{R}}^ N\) where N is the dimension of \({\mathfrak g}_{M,r}\). As an application they solve explicitly the control problem associated to the corresponding vectorfields in the case \(M=2\).
scientific article; zbMATH DE number 4181583
scientific article