Abstract
This article describes module extensions of 3-Lie algebras. In particular, we introduce the notion of T
θ-extensions and -extensions of 3-Lie algebras in terms of modules. We then provide the necessary and sufficient conditions for a 2k-dimensional metric 3-Lie algebra to be isomorphic to a T
θ-extension. We also study properties of the
-extension of nilpotent metric 3-Lie algebras. At the end of this article, we obtain all the
-extensions of four-dimensional 3-Lie algebras.
Keywords:
Acknowledgement
This project is partially supported by NSF(10871192) of China and NSF(A2010000194) of Hebei Province, China.