Invertible Linear Maps on Simple Lie Algebras Preserving Solvability
Invertible Linear Maps on Simple Lie Algebras Preserving Solvability
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DOI：
10.1080/00927872.2012.740643
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发表时间：
2014-03
影响因子：
0.7
通讯作者：
Dengyin Wang;Shikun Ou;Xiaoxiang Yu
中科院分区：
文献类型：
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作者：
Dengyin Wang;Shikun Ou;Xiaoxiang Yu
设是一个（有限维）秩为l的复单李代数。一个可逆的线性映射在上被称为在两个方向上保持可解性，如果和−1将每个可解的子代数发送到某个可解的子代数。本文证明了n上可逆线性映射保持双向可解的充要条件是它可以分解为一个内自同构、一个图自同构、一个标量乘映射和一个对角自同构的乘积.
Let 𝔤 be a (finite-dimensional) complex simple Lie algebra of rank l. An invertible linear map ϕ on 𝔤 is said to preserve solvability in both directions if ϕ, as well as ϕ−1, sends every solvable subalgebra to some solvable one. In this article, it is shown that an invertible linear map ϕ 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.