Some Complete Lie Algebras Original Research Article

We give the derivation algebra Der Hand the holomorph image(H) of the finite dimensional Heisenberg algebraHover the complex fieldC. We also give the derivation algebra Der image(H) of image(H). We prove that Der(H) is a simple complete Lie algebra, image(H) is not a complete Lie algebra, but its derivation algebra Der image(H) is a simple complete Lie algebra.