@Article{CMR-28-1,
author = {Zhengxin, Chen and Qiong, Chen},
title = {Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability},
journal = {Communications in Mathematical Research },
year = {2012},
volume = {28},
number = {1},
pages = {26--42},
abstract = {<p style="text-align: justify;">Let $M_n$ be the algebra of all $n × n$ complex matrices and $gl(n, \mathbb{C})$ be
the general linear Lie algebra, where $n ≥ 2$. An invertible linear map $ϕ: gl(n, \mathbb{C}) →
gl(n, \mathbb{C})$ preserves solvability in both directions if both $ϕ$&nbsp;and $ϕ^{−1}$ map every solvable
Lie subalgebra of $gl(n, \mathbb{C})$ to some solvable Lie subalgebra. In this paper we classify
the invertible linear maps preserving solvability on $gl(n, \mathbb{C})$ in both directions. As a
sequence, such maps coincide with the invertible linear maps preserving commutativity on $M_n$ in both directions.</p>},
issn = {2707-8523},
doi = {https://doi.org/2012-CMR-19067},
url = {https://global-sci.com/article/81820/invertible-linear-maps-on-the-general-linear-lie-algebras-preserving-solvability}
}