Lie n-algebra

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.
• John Baez, Alissa Crans, Higher-Dimensional Algebra VI: Lie 2-Algebras Theory and Applications of Categories, Vol. 12, (2004) No. 15, pp 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