THE NATURAL CLASSIFICATION OF REAL LIE ALGEBRAS

M. Rainer and H.-J. Schmidt

Key words: Real Lie algebras, homogeneous Riemannian manifolds,
general topology

1991 Math. Subject Classification: 53B20, 22E15.

Abstract: We classify the $n$-dimensional
real Lie algebras according to algebraic, geometric,
and topological points of view. For the case that Lie algebra,
Riemannian geometry, and general topology yield the same
classification we call it the natural one.
It turns out that for dimension $n\leq 3$ our classification
is natural. For $n\geq 4$ partial results are given.