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Volume 28, Issue 3
Non-Linear Invertible Maps that Preserve Staircase Subalgebras

Yanxia Zhao & Yuling Xia

Commun. Math. Res., 28 (2012), pp. 265-274.

Published online: 2021-05

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  • Abstract

Let $\mathcal{g}$ 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 $φ : \mathcal{g} → \mathcal{g}$ 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.

  • Keywords

general linear Lie algebra, staircase subalgebra, non-linear map.

  • AMS Subject Headings

15A04, 15A27, 17B30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-28-265, author = {Zhao , Yanxia and Xia , Yuling}, title = {Non-Linear Invertible Maps that Preserve Staircase Subalgebras}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {3}, pages = {265--274}, abstract = {

Let $\mathcal{g}$ 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 $φ : \mathcal{g} → \mathcal{g}$ 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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19046.html} }
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 -

Let $\mathcal{g}$ 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 $φ : \mathcal{g} → \mathcal{g}$ 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.

Zhao , Yanxia and Xia , Yuling. (2021). Non-Linear Invertible Maps that Preserve Staircase Subalgebras. Communications in Mathematical Research . 28 (3). 265-274. doi:
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