Word.ws English Dictionary

Jacobi identity

Jacobi identity noun: 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.

Noun

Jacobi identity (countable and uncountable, plural Jacobi identities)

  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.
    • 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
    • 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.2004, James Lepowsky, Haisheng Li, Introduction to Vertex Operator Algebras and Their Representations, Springer (Birkhäuser), page 12

Forms of Jacobi identity

pluralJacobi identities

Origin of Jacobi identity

After German mathematician Carl Gustav Jakob Jacobi (1804-1851).

Words formed from Jacobi identity

  • super Jacobi identity

Questions about Jacobi identity

What does Jacobi identity mean?
Jacobi identity means 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.
What part of speech is Jacobi identity?
Jacobi identity is a noun.
What is the plural of Jacobi identity?
The plural of Jacobi identity is Jacobi identities.

Words near Jacobi identity in the dictionary

  1. Jacobethan
  2. Jacobi
  3. Jacobi ellipsoid
  4. Jacobi ellipsoids
  5. Jacobi identities
  6. Jacobi identity
  7. Jacobi polynomial
  8. Jacobi polynomials
  9. Jacobi symbol
  10. Jacobi symbols
  11. jacobian

Source and license

Adapted from Wiktionary: Jacobi identity (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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