$(\mu, \rho, \beta)$-Extension of $3$-Lie algebras
  We study an extension algebra $A$ from two given $3$-Lie algebras $M$ and $H$, and discuss the extensibility of a pair of derivations, one from the derivation algebra of $M$ and the other from that of $H$, to a derivation of $A$. In particular, we give conditions for such an extension to be a $3$-Lie algebra, and provide necessary and sufficient conditions of the pair of derivations to be extendable. 
Ruipu Bai, Yansha Gao, Zhenheng Li
math.RA