Invertible Linear Maps on Simple Lie Algebras Preserving Solvability |
| |
| Authors: | Dengyin Wang Shikun Ou Xiaoxiang Yu |
| |
| Affiliation: | 1. School of Science , China University of Mining and Technology , Xuzhou , China wdengyin@126.com;3. School of Science , Jianxi University of Science and Technology , Ganzhou , China;4. School of Mathematical Sciences , Xuzhou Normal University , Xuzhou , China |
| |
| Abstract: | Let 𝔤 be a (finite-dimensional) complex simple Lie algebra of rank l. An invertible linear map ? on 𝔤 is said to preserve solvability in both directions if ?, as well as ??1, sends every solvable subalgebra to some solvable one. In this article, it is shown that an invertible linear map ? on 𝔤 preserves solvability in both directions if and only if it can be decomposed into the product of an inner automorphism, a graph automorphism, a scalar multiplication map and a diagonal automorphism. |
| |
| Keywords: | Automorphisms of Lie algebras Simple Lie algebra Solvability |
|
|
