Property Of Lie Algebra So~*(2n) And G~*(m, S, C)

In this paper, we study two kinds of typical Lie algebra which is special orthogonal star Lie algebra and g * (m, S, C) Lie algebra. In the first it has been introduced that some basic knowledge of Lie algebra and the structure of the two typical types of Lie Algebras. Then we study the typical property of theirs form the starting of nature and constitute of the two types of Lie algebra (i.e., base), and we calculated separately their dimension, center, commutator algebra, Killing type, Cartan subalgebra, structure formula, root system, and so on.In this paper, the following theorems have been mainly proved:Theorem A: The center of so *(2 n ) is 0, and the center of g *( m , S , C ) is {a iI ma∈R}.Theorem B: Both so *(2 n ) and g *( m, S , C ) are not simple Lie algebra.Theorem C: The commutator algebra of so *(2 n ) is its own, and the commutator algebra ofand the commutator algebra of Theorem D: The Cartan subalgebra ofand the Cartan subalgebra of Theorem E: The structural formula of...