Journal of Lie Theory 34 (2024), No. 3, 595--610
Copyright Heldermann Verlag 2024
2-Local Derivations on the Centerless Ovsienko-Roger Algebra
Yan Liu
School of Mathematics and Statistics, Northeast Normal University, Changchun, China
liuy726@nenu.edu.cn
Yao Ma
School of Mathematics and Statistics, Northeast Normal University, Changchun, China
may703@nenu.edu.cn
Liangyun Chen
School of Mathematics and Statistics, Northeast Normal University, Changchun, China
chenly640@nenu.edu.cn
[Abstract-pdf]
We study 2-local derivations on the centerless Ovsienko-Roger algebra $\mathfrak{L_{\lambda}}$, which is the semi-direct product of the Witt algebra and its tensor density module. We prove that every 2-local derivation on $\mathfrak{L_{\lambda}}$ is a derivation for $\lambda\in \mathbb{C}\setminus\{0,1,2\}$. We divide into two cases to consider 2-local derivations on $\mathfrak{L_{\lambda}}$ depending on whether the parameter $\lambda$ is an integer, that is for the case $\lambda\in \mathbb{Z}\setminus\{0,1,2\}$ and the case $\lambda\notin \mathbb{Z}$.
Keywords: Centerless Ovsienko-Roger algebra, derivation, 2-local derivation.
MSC: 17B05, 17B40, 17B65.
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