In mathematics, a Lie n-algebra is a generalization of a Lie algebra, a vector space with a bracket, to higher order operations. For example, in the case of a Lie 2-algebra, the Jacobi identity is replaced by an isomorphism called a Jacobiator.
See also 2-ring Homotopy Lie algebra
References
Jim Stasheff and Urs Schreiber, Zoo of Lie n-Algebras. A post about the paper at the n-category café. Baez, John; Crans, Alissa (2004). "Higher-Dimensional Algebra VI: Lie 2-Algebras". Theory and Applications of Categories. 12 (15): 492–528.
Further reading https://ncatlab.org/nlab/show/Lie+2-algebra https://golem.ph.utexas.edu/category/2007/08/string_and_chernsimons_lie_3al.html