English Dictionary

Jacobi identity

noun

(mathematics) 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.

The Jacobi identity is a fundamental property in mathematics.

意味（1）

(mathematics) 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.

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