IMCS/Publications/BASM/Issues/BASM n.3 (70), 2012/

A Note on the Affine Subspaces of Three-Dimensional Lie Algebras

Authors: Rory Biggs, Claudiu C. Remsing
Keywords: A±ne subspace, Lie algebra, the Bianchi-Behr classification, left-invariant control system, detached feedback equivalence.


A classification of full-rank a±ne subspaces of (real) three-dimensional Lie algebras is presented. In the context of invariant control a±ne systems, this is exactly a classification of all full-rank systems evolving on three-dimensional Lie groups.

Dept. of Mathematics (Pure and Applied)
Rhodes University, PO Box 94
6140 Grahamstown, South Africa
E-mail: ,


Adobe PDF document0.18 Mb