Models for free nilpotent Lie algebras. (English) Zbl 0717.17006
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 \(M=2\).
Reviewer: J.Hilgert
MSC:
| 17B01 | Identities, free Lie (super)algebras |
| 93B29 | Differential-geometric methods in systems theory (MSC2000) |
| 17B30 | Solvable, nilpotent (super)algebras |
| 17B66 | Lie algebras of vector fields and related (super) algebras |
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