Jacobi identity

Etymology
After German mathematician (1804-1851).

Noun

 * 1)  Given a binary operation × defined on a set S which also has additive operation + and additive identity 0, the property that a × (b×c) + b × (c×a) + c × (a×b) = 0 for all a, b, c in S.
 * 2) * 2004, ames Lepowsky, Haisheng Li, Introduction to Vertex Operator Algebras and Their Representations, Springer (Birkhäuser), page 12,
 * As we have already mentioned, the Jacobi identity is actually the generating function of an infinite list of generally highly nontrivial identities, and one needs many of these individual componenent identities in working with the theory.
 * As we have already mentioned, the Jacobi identity is actually the generating function of an infinite list of generally highly nontrivial identities, and one needs many of these individual componenent identities in working with the theory.

Usage notes
Often stipulated as an axiom. Notably applicable to the cross product in a vector space and to the Lie bracket operation in a Lie algebra.

Translations

 * Italian: identità di Jacobi