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 - <p style="text-align: justify;">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.</p>