TY - JOUR
T1 - Non-Linear Invertible Maps that Preserve Staircase Subalgebras
AU - Zhao , Yanxia
AU - Xia , Yuling
JO - Communications in Mathematical Research 
VL - 3
SP - 265
EP - 274
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19046.html
KW - general linear Lie algebra, staircase subalgebra, non-linear map.
AB - <p style="text-align: justify;">Let&nbsp;$\mathcal{g}$&nbsp;be the general linear Lie algebra consisting of all $n × n$ matrices
over a field $F$ and with the usual bracket operation $[x, y] = xy − yx$. An invertible
map $φ&nbsp;: \mathcal{g} → \mathcal{g}$ is said to preserve staircase subalgebras if it maps every staircase
subalgebra to some staircase subalgebra of the same dimension. In this paper, we
devote to giving an explicit description on the invertible maps on $\mathcal{g}$ that preserve
staircase subalgebras.</p>