@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} }