Volume 18, Issue 1, March 2011, Pages 151 - 160
Derivations of the 3-Lie Algebra Realized by gl(n, ℂ)
Authors
Ruipu Bai*, ‡, Jinxiu Wang†, ‡
College of Mathematics and Computer Science, Hebei University, Baoding 071002, China
Zhenheng Li
Department of Mathematical Sciences, University of South Carolina Aiken, Aiken, SC 29801, USA,zhenhengl@usca.edu
‡
Project partially supported by NSF(10871192) of China and NSF(A2010000194) of Hebei Province, China.
Received 24 June 2010, Accepted 25 September 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001222How to use a DOI?
- Keywords
- 3-Lie algebra; derivation algebra; inner derivation algebra; realization
- Abstract
This paper studies structures of the 3-Lie algebra M realized by the general linear Lie algebra gl(n, ℂ). We show that M has only one nonzero proper ideal. We then give explicit expressions of both derivations and inner derivations of M. Finally, we investigate substructures of the (inner) derivation algebra of M.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Ruipu Bai AU - Jinxiu Wang AU - Zhenheng Li PY - 2021 DA - 2021/01/07 TI - Derivations of the 3-Lie Algebra Realized by gl(n, ℂ) JO - Journal of Nonlinear Mathematical Physics SP - 151 EP - 160 VL - 18 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001222 DO - 10.1142/S1402925111001222 ID - Bai2021 ER -