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Jacobi identity

Property of some binary operations, such as the cross product and any ring's commutator
Intangible Theorem Q1151539

Facts

5 properties
Instance of
theorem
Defining formula
a \times (b \times c) + c \times (a \times b) + b \times (c \times a) = 0\quad \forall{a,b,c}\in S
Maintained by WikiProject
WikiProject Mathematics[4]
Named after
Carl Gustav Jacob Jacobi[2]
Studied by
category theory[3]
🏷️ Also known as
en Jacobi identity de Jacobische Identität de Jacobi-Identität es identidad de Jacobi fr relation de Jacobi fr identité de Jacobi id indentitas Jacobi it identità di Jacobi ja ヤコビの恒等式 ja ヤコビ恒等式 ko 야코비 항등식 nl Jacobi-identiteit pt identidade de Jacobi ro identitatea lui Jacobi ru тождество Якоби sv Jacobi-identiteten tr Jakobi özdeşliği uk тотожність Якобі zh 雅可比恒等式 zh 雅戈比恒等式
🔖 Identifiers · 15
Library of Congress Authorities ID
sh93005729
GND ID
4348111-5
OpenAlex ID
C206159579
Bibliothèque nationale de France ID
166168973
Freebase ID
/m/01r067
Group Properties article ID
Jacobi_identity
IdRef ID
162368402
J9U entity ID
987007534634305171
MathWorld ID
JacobiIdentities
Microsoft Academic ID (discontinued)
206159579
NLab ID
Jacobi identity
Open Library subject ID
jacobi_identity
Show all 15 identifiers +3
Quora topic ID
Jacobi-Identity
Treccani's Enciclopedia della Matematica ID
identita-di-jacobi
Yale LUX ID
concept/e87d05db-505b-4119-8ede-44746273fd11

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🔗 Connections
Created notable works 1
Carl Gustav Jacob Jacobi
Instance of 1
theorem
Maintained by WikiProject 1
WikiProject Mathematics
Named after 1
Carl Gustav Jacob Jacobi
Studied by 1
category theory
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Summary

Jacobi identity is a theorem[1].

Related Entities

Carl Gustav Jacob Jacobi

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

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Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Jacobi identity. Retrieved November 10, 2026, from https://4ort.xyz/entity/jacobi-identity
MLA “Jacobi identity.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Nov. 2026, https://4ort.xyz/entity/jacobi-identity.
BibTeX @misc{4ortxyz_jacobi-identity_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Jacobi identity}}, year = {2026}, url = {https://4ort.xyz/entity/jacobi-identity}, note = {Accessed: 2026-11-10}}
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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 24w ago · Twofivesixbot bot · 2026-05-26 view diff on Wikidata ↗
    Instance of → theorem
    Maintained by WikiProject → WikiProject Mathematics
    Named after → Carl Gustav Jacob Jacobi
    Studied by → category theory
    "Changed claim qualifiers: J9U entity ID: 987007534634305171, mv to monolingual text names on J9U statements"
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