THE CONSTRUCTION OF SOLVABLE LIE-ALGEBRAS FROM EQUIDIMENSIONAL NILPOTENT ALGEBRAS

The study of gradings of solvable Lie algebras L of finite dimensionover a field F of zero characteristic led the authors to the discovery of equidimensional nilpotent algebras L* uniquely determined by L up to F-isomorphy. Conversely, for any finite dimensional Lie algebra L* over F an algorithm is developed which yields in parametric form all solvable Lie algebras L determiningL* as the corresponding nilpotent algebra. The exposition is independent of Lie grading theory. It organizes in a novel way the classification of solvable Lie algebras of given dimension around the same task for nilpotent algebras. Every isomorphy class of solvable F-algebras is obtained in this way. © 1990.