Phrase guide

Jacobi identity

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

noun

Meaning 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.

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Topics: mathematics, sciences

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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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

Across languages

Translations

2 source translations are retained for this English entry.

  • Italian: identità di Jacobi — property of a binary operation
  • Polish: tożsamość Jacobiego — property of a binary operation