Centralizers Of Elements Of Graded Cartan Type Lie Algebras

In semisimple Lie algebras over an algebraically closed field with characteristic zero, it’s Cartan subalgebras are precisely the maximal toral subalgebras, they are all commuta-tive and are centralizers of some regular element, so it’s important to know the centralizers of element, Shu Bin and Yao Yu-feng get the decomposition of nilpotent orbits of the Witt algebras W1 by investigate detailedly it’s automorphism groups, after it, Yao and Chang Hao put the decomposition as the important lemma of the paper’s central result in the nilpotent commuting variety of the Witt algebra. In general, it’s hard to describe the centralizer, be-cause the automorphism groups of Cartan type Lie algebras are very complicated, it was mentioned in there’s dissertation.In this article, we get the centralizer of derivation that is not nilpotent of Witt algebra and graded zero in part with graded zero, and some nongraded derivation etc. We hope that this can help people who will use these results.