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.