The five-dimensional complete left-symmetric algebra structures compatible with an Abelian Lie algebra structure

The classification of five-dimensional complete left-symmetric algebras is known to be a hard problem. In this paper we establish an explicit classification of the five-dimensional complete left-symmetric algebras over R, having an abelian associated Lie algebra. A detailed list of all possible isomorphism types is presented. (C) 1997 Elsevier Science Inc.