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Volume 25, Issue 1
The Lie Algebras in which Every Subspace Is Its Subalgebra

Mingzhong Wu

Commun. Math. Res., 25 (2009), pp. 1-8.

Published online: 2021-05

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  • Abstract

In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to $g\dot{+}\mathbb{C}id_g$, where $g$ is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.

  • Keywords

HB Lie algebra, complete Lie algebra, holomorph.

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-1, author = {Mingzhong and Wu and and 18096 and and Mingzhong Wu}, title = {The Lie Algebras in which Every Subspace Is Its Subalgebra}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {1}, pages = {1--8}, abstract = {

In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to $g\dot{+}\mathbb{C}id_g$, where $g$ is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19070.html} }
TY - JOUR T1 - The Lie Algebras in which Every Subspace Is Its Subalgebra AU - Wu , Mingzhong JO - Communications in Mathematical Research VL - 1 SP - 1 EP - 8 PY - 2021 DA - 2021/05 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19070.html KW - HB Lie algebra, complete Lie algebra, holomorph. AB -

In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to $g\dot{+}\mathbb{C}id_g$, where $g$ is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.

Mingzhong Wu. (2021). The Lie Algebras in which Every Subspace Is Its Subalgebra. Communications in Mathematical Research . 25 (1). 1-8. doi:
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