Affine Subspaces of the Lie Algebra se(1,1)

Abstract

We classify the full-rank affine subspaces (resp. parametrized affine subspaces) of the semi-Euclidean Lie algebra se(1,1). The equivalence relations under consideration (L-equivalence and P-equivalence) are motivated by the study of invariant control affine systems. Exhaustive lists of equivalence representatives are obtained, along with classifying conditions.