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Could somebody (simply) explain the basics foundations of Lie 2-algebras, and some basic practical applications ?

For instance, does it exist a 3-map (equivalent to the 2-map commutator for Lie algebras), with :

$ [T_a, T_b, T_c] = f_{abc}^d T_d $

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    @Qiaochu Yuan: Thanks. Is there any relation between the two (Lie triple system and Lie 2-algebra) ?2012-10-27

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