Geodesic
Biderivations of Lie algebras
Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 440-450

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DOI

In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras including finite-dimensional simple Lie algebras over arbitrary fields of characteristic not $2$ or $3$, and the Witt algebras $\mathcal {W}^+_n$ over fields of characteristic $0$. As an application, commutative post-Lie algebra structure on the aforementioned Lie algebras is shown to be trivial.
DOI : 10.4153/S0008439524000833
Mots-clés : Symmetric biderivation, Witt algebra, finite-dimensional simple Lie algebra, symmetric radical, characteristic subalgebra 
Chen, Qiufan; Yao, Yufeng; Zhao, Kaiming. Biderivations of Lie algebras. Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 440-450. doi: 10.4153/S0008439524000833
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     author = {Chen, Qiufan and Yao, Yufeng and Zhao, Kaiming},
     title = {Biderivations of {Lie} algebras},
     journal = {Canadian mathematical bulletin},
     pages = {440--450},
     year = {2025},
     volume = {68},
     number = {2},
     doi = {10.4153/S0008439524000833},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000833/}
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