Maurer–Cartan form

on a Lie group G, a canonical 1-form valued in its own Lie algebra; the unique principal-bundle connection on the unique G-bundle over the one-point space
Thing one_form Q552787
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Maurer–Cartan form

Summary

Maurer–Cartan form is a one-form[1]. It draws 134 Wikipedia views per month (one_form category, ranking #1 of 1).[2]

Key Facts

  • Maurer–Cartan form's instance of is recorded as one-form[3].
  • Maurer–Cartan form's instance of is recorded as Lie algebra-valued differential form[4].
  • Maurer–Cartan form's instance of is recorded as principal bundle connection[5].
  • Maurer–Cartan form's instance of is recorded as mathematical concept[6].
  • Ludwig Maurer is named after Maurer–Cartan form[7].
  • Élie Cartan is named after Maurer–Cartan form[8].
  • Maurer–Cartan form's studied by is recorded as category theory[9].
  • Maurer–Cartan form's maintained by WikiProject is recorded as WikiProject Mathematics[10].

Body

Definition and Type

Recorded instance of include one-form[3], Lie algebra-valued differential form[4], principal bundle connection[5], and mathematical concept[6].

Origins

Things named after include Ludwig Maurer[7], a mathematician[11], 1859–1927[12], of Germany[13] and Élie Cartan[8], a mathematician[14], 1869–1951[15], of France[16], awarded the Leconte Prize[17], specialised in differential geometry[18].

Why It Matters

Maurer–Cartan form draws 134 Wikipedia views per month (one_form category, ranking #1 of 1).[2] It has Wikipedia articles in 9 language editions, a strong signal of global cultural recognition.[19] It is known by 14 alternative names across languages and contexts.[20]

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] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.

Inline context (facts about related entities)

  1. [11] ↑ . Wikidata. wikidata.org. → on this site
  2. [12] ↑ . Wikidata. wikidata.org. → on this site
  3. [13] ↑ . Wikidata. wikidata.org. → on this site
  4. [14] ↑ . Wikidata. wikidata.org. → on this site
  5. [15] ↑ . Wikidata. wikidata.org. → on this site
  6. [16] ↑ . Wikidata. wikidata.org. → on this site
  7. [17] ↑ . Wikidata. wikidata.org. → on this site
  8. [18] ↑ . Wikidata. wikidata.org. → on this site

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [19] ↑ . Wikidata sitelinks. wikidata.org.
  3. [20] ↑ . 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). Maurer–Cartan form. Retrieved October 5, 2026, from https://4ort.xyz/entity/maurer-cartan-form
MLA “Maurer–Cartan form.” 4ort.xyz Knowledge Graph, 4ort.xyz, 5 Oct. 2026, https://4ort.xyz/entity/maurer-cartan-form.
BibTeX @misc{4ortxyz_maurer-cartan-form_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Maurer–Cartan form}}, year = {2026}, url = {https://4ort.xyz/entity/maurer-cartan-form}, note = {Accessed: 2026-10-05}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Maurer–Cartan form — https://4ort.xyz/entity/maurer-cartan-form (retrieved 2026-10-05)

Canonical URL: https://4ort.xyz/entity/maurer-cartan-form · Last refreshed:

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. 24d ago · Ferran Mir · 2026-09-13 view diff on Wikidata ↗
    Studied by → category theory
    Instance of → one-form, Lie algebra-valued differential form, principal bundle connection +1
    Named after → Ludwig Maurer, Élie Cartan
    Maintained by wikiproject → WikiProject Mathematics
    + 3 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ [[Property:P31]]: [[Q24034552]]"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.