Jacobi identity

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

Summary

Jacobi identity is a theorem[1]. It draws 164 Wikipedia views per month (theorem category, ranking #145 of 1,306).[2]

Key Facts

  • Jacobi identity's instance of is recorded as theorem[3].
  • Carl Gustav Jacob Jacobi is named after Jacobi identity[4].
  • Jacobi identity's GND ID is recorded as 4348111-5[5].
  • Jacobi identity's Library of Congress authority ID is recorded as sh93005729[6].
  • Jacobi identity's Bibliothèque nationale de France ID is recorded as 166168973[7].
  • Jacobi identity's IdRef ID is recorded as 162368402[8].
  • Jacobi identity's Freebase ID is recorded as /m/01r067[9].
  • Jacobi identity's defining formula is recorded as a \times (b \times c) + c \times (a \times b) + b \times (c \times a) = 0\quad \forall{a,b,c}\in S[10].
  • Jacobi identity's studied by is recorded as category theory[11].
  • Jacobi identity's MathWorld ID is recorded as JacobiIdentities[12].
  • Jacobi identity's Quora topic ID is recorded as Jacobi-Identity[13].
  • Jacobi identity's Open Library subject ID is recorded as jacobi_identity[14].
  • Jacobi identity's nLab ID is recorded as Jacobi identity[15].
  • Jacobi identity's maintained by WikiProject is recorded as WikiProject Mathematics[16].
  • Jacobi identity's Microsoft Academic ID is recorded as 206159579[17].
  • Jacobi identity's National Library of Israel J9U ID is recorded as 987007534634305171[18].
  • Jacobi identity's Group Properties article ID is recorded as Jacobi_identity[19].
  • Jacobi identity's Treccani's Enciclopedia della Matematica ID is recorded as identita-di-jacobi[20].
  • Jacobi identity's OpenAlex ID is recorded as C206159579[21].
  • Jacobi identity's Yale LUX ID is recorded as concept/e87d05db-505b-4119-8ede-44746273fd11[22].

Why It Matters

Jacobi identity draws 164 Wikipedia views per month (theorem category, ranking #145 of 1,306).[2] It has Wikipedia articles in 15 language editions, a strong signal of global cultural recognition.[23] It is known by 4 alternative names across languages and contexts.[24]

References

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

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . Integrated Authority File. Retrieved . wikidata.org.
  4. [6] . Library of Congress Subject Headings. Retrieved . wikidata.org.
  5. [7] . Library of Congress Subject Headings. Retrieved . wikidata.org.
  6. [8] . IdRef. Retrieved . wikidata.org.
  7. [9] . Freebase Data Dumps. wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . Quora. wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . National Library of Israel Names and Subjects Authority File. wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.
  20. [22] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [23] . Wikidata sitelinks. wikidata.org.
  3. [24] . Wikidata aliases. wikidata.org.

📑 Cite this page

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 May 3, 2026, from https://4ort.xyz/entity/jacobi-identity
MLA “Jacobi identity.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 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: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Jacobi identity — https://4ort.xyz/entity/jacobi-identity (retrieved 2026-05-03)

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