Some Results Of The Two-dimensional Subalgebras Of The Virasoro Algebra And The Lie Algebra L (z, F, ¦Ä), Semi-simple,

It concludes two articles, in my first paper 玶esults of virasoro algebra two dimension algebra? It is in 1909 that virasoro algebra of no centre came up . E. cartan define the virasoro algebra . A lot of scholars study the algebra and find much results, For example ,it is verify that the algebra is simple algebra. But it is a question how to decide two demensional subalgebra. In my paper, we make use of coefficient matrix, and then we can prove that Virasoro algebra has no two dimensional commutative subalgehra. it is very esay to verify that d0 and d~ can span subalgebra ,But we find a lot of very interesting two dimensional suhalgebra. My second paper 玸emi梥imple of lie algebra L(Z~ f, ~5)? Some scholars study a lot of infinite dimension lie algebra recently. For example Professor Kaiming Zhao and Professor J. Marshall. Obsorn Study a called L梥hape lie subalgebra and publish some papers. They propose following two open questions in recent. (I). How to decide centralizer of any element in simple lie algebra in L(A.?.a): (2). How to decide centralizer of e0 in General lie algebra. L(A.?a). A is an abelian group in their paper , integer additive group Z is in place of A in my paper. We use coefficient matrix and maximal element and then we can prove that lie algebra L(Z, f, o) is semi梥imple lie algebra and we give other some property in this algebra and then we answer the two open questions at the end.