TY - JOUR
T1 - Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability
AU - Chen , Zhengxin
AU - Chen , Qiong
JO - Communications in Mathematical Research 
VL - 1
SP - 26
EP - 42
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19067.html
KW - general linear Lie algebra, solvability, automorphism of Lie algebra.
AB - <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>