Non-Linear Invertible Maps that Preserve Staircase Subalgebras (Communications in Mathematical Research, 2021)
Let $\mathcal{g}$ be the general linear Lie algebra consisting of all $n × n$ matricesover a field $F$ and with the usual bracket operation $[x, y] = xy − yx$. An invertiblemap $φ : \mathcal{g} → \mathcal{g}$ is said to preserve staircase subalgebras if it maps every staircasesubalgebra to some staircase subalgebra of the same dimension. In this paper, wedevote to giving an explicit description on the invertible maps on $\mathcal{g}$ that preservestaircase subalgebras.
Keywords: general linear Lie algebra; staircase subalgebra; non-linear map.