2-Local Derivations on the Centerless Ovsienko-Roger Algebra

Y. Liu ; Y. Ma ; L. Chen

Journal of Lie theory, Tome 34 (2024) no. 3, pp. 595-61

Résumé

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 $\lambda\notin \mathbb{Z}$.

Détail

Classification : 17B05, 17B40, 17B65
Mots-clés : Centerless Ovsienko-Roger algebra, derivation, 2-local derivation