$(\mu, \rho, \beta)$-Extension of $3$-Lie algebras

27 Jul 2016  ·  Bai Ruipu, Gao Yansha, Li Zhenheng ·

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...

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Rings and Algebras