The construction of solvable lie algebras from equidimensional nilpotent algebras

AbstractThe 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