arrow
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

Export citation
  • 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.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMR-25-1, author = {Wu , Mingzhong}, 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.

Wu , Mingzhong. (2021). The Lie Algebras in which Every Subspace Is Its Subalgebra. Communications in Mathematical Research . 25 (1). 1-8. doi:
Copy to clipboard
The citation has been copied to your clipboard