The Killing Model And Ideal Of (p, Q) Form Lorentz Lie Algebra Over Rings

Let R be a commutative ring with 1.In the paper,we get the basis of(p,q) type Lorentz Lie algebra first and know the structure of this kind of Lie algebra clearly. In the bases,this paper gives a simple formula to compute the killing form of(p,q) type Lorentz Lie algebra.Then,the undegeneration of the killing form is proved.In the third part,we describe the order ideal of(p,q) type Lorentz Lie algebra and have three lemmas.Thus,we prove that all the ideals of(p,q) type Lorentz Lie algebra are standard if 2 is an unit of the ring.