For Three-solution-type Non-degenerate Lie Algebras And Their Derivation Lie Algebra Structure

In this paper, we first present two types of the solvable Lie Algebras with non-degenerate invariant bilinear form. One is extended Heisenberg Lie Algebra, the other is 3-solvable non-degenerate Lie Algebra. Furthermore, we give one equivalent condition and an example of the later type. We completely determined the structure of Derg of the 3- solvable non-degenerate Lie Algebra, g .