CENTRAL EXTENSIONS OF THE SMALL-DIMENSIONAL SOLVABLE LIE ALGEBRA

Abstract

In this thesis, it is necessary to consider the filtered cohomology structure relative to the ideals of the lower central series: a cocycle defining the central extension is needed has maximum filtration. Such a geometric method allows us to classify nilpotent Lie algebras small dimensions, as well as for classifying Lie algebras of narrow natural rank. Concept a rigid central extension is introduced. Examples of rigid and non-rigid central extensions built.