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The Lie Algebras in which Every Subspace Is Its Subalgebra |
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| Authors: | Mingzhong Wu |
| Abstract: | In this paper, we study the Lie algebras in which every subspace is itssubalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra isan HB Lie algebra if and only if it is isomorphic to $gdot{+}mathbb{C}id_g$, where $g$ is an abelianLie algebra. Moreover we show that the derivation algebra and the holomorph of anonabelian HB Lie algebra are complete. |
| Keywords: | HB Lie algebra complete Lie algebra holomorph. |
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