Jacobi identity

plural Jacobi identities

1. countableuncountablemathematicsGiven 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.

   We give here two proofs of the Jacobi identity for the generalized Poisson bracket defined in Eq. (13.69a).

   1995, Stephen L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, page 535

   2 more examples

   2004, James 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.

   It is sufficient to test the Jacobi identity against three linear functions [354] (this reference also provides a code for evaluating Jacobi identities).

   2005, Martin Kröger, Models for Polymeric and Anisotropic Liquids, Springer, page 113