Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 :

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

share|improve this question
What you describe is not a Lie 2-algebra, it is a Lie triple system (en.wikipedia.org/wiki/Triple_system#Lie_triple_systems). A Baez-Crans Lie 2-algebra is a Lie algebra internal to the category of 2-term chain complexes. –  Qiaochu Yuan Oct 27 '12 at 18:10
@Qiaochu Yuan: Thanks. Is there any relation between the two (Lie triple system and Lie 2-algebra) ? –  Trimok Oct 27 '12 at 18:13

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.