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Three classes of 3-Lie algebras

BAI Ruipu, ZHANG Yinghua and GAO Yansha

This paper studies three classes of 3-Lie algebras which are realized by bilinear functions on vector spaces. The solvability, nilpotency and metric structures of 3-Lie algebras are discussed. And structures of inner derivation algebras and derivation algebras are investigated. The results can be used in the realization of 3-Lie algebras.