Algorithms for central extensions of Lie algebras

Abstract

It follows from [1] that every n-dimensional nilpotent Lie algebra is a central extension of a lower dimensional nilpotent Lie algebra. This paper develops algorithms to handle two problems: (1) the decomposition of a given nilpotent Lie algebra @@@@ as a finite sequence of central extensions of lower dimensional nilpotent Lie algebras and (2) the construction of all n-dimensional nilpotent Lie algebras as central extensions of lower dimensional nilpotent Lie algebras.