bialgebra

vector space which is both a unital associative algebra and a counital coassociative coalgebra in a compatible way
Thing general Q494141
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bialgebra

Summary

bialgebra ranks in the top 2% of general entities by monthly Wikipedia readership (61 views/month).[1]

Key Facts

  • bialgebra's GND ID is recorded as 4316695-7[2].
  • bialgebra's subclass of is recorded as algebra over a field[3].
  • bialgebra's subclass of is recorded as coalgebra[4].
  • bialgebra's subclass of is recorded as quasi-bialgebra[5].
  • bialgebra's Freebase ID is recorded as /m/01t59s[6].
  • bialgebra's defining formula is recorded as \begin{aligned}\Delta\circ\nabla&=\nabla\otimes\nabla\circ(\operatorname{id}\otimes\sigma\otimes\operatorname{id})\circ\Delta\otimes\Delta\\epsilon\otimes\epsilon&=\epsilon\circ\nabla\\eta\otimes\eta&=\Delta\circ\eta\\epsilon\circ\eta&=\operatorname{id} \end{aligned}[7].
  • bialgebra's studied by is recorded as abstract algebra[8].
  • bialgebra's BabelNet ID is recorded as 02460786n[9].
  • bialgebra's nLab ID is recorded as bialgebra[10].
  • bialgebra's schematic is recorded as Bialgebra2.svg[11].
  • bialgebra's schematic is recorded as Bialgebra3.svg[12].
  • bialgebra's schematic is recorded as Bialgebra4a.svg[13].
  • bialgebra's schematic is recorded as Bialgebra1.svg[14].
  • bialgebra's maintained by WikiProject is recorded as WikiProject Mathematics[15].
  • bialgebra's Microsoft Academic ID is recorded as 2778676360[16].
  • bialgebra's Group Properties article ID is recorded as Bialgebra[17].
  • bialgebra's OpenAlex ID is recorded as C2778676360[18].

Why It Matters

bialgebra ranks in the top 2% of general entities by monthly Wikipedia readership (61 views/month).[1] bialgebra has Wikipedia articles in 9 language editions, a strong signal of global cultural recognition.[19] bialgebra is known by 3 alternative names across languages and contexts.[20]

References

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

Direct Wikidata claims

  1. [2] . wikidata.org.
  2. [3] . Hopf Algebras. wikidata.org.
  3. [4] . Hopf Algebras. wikidata.org.
  4. [5] . wikidata.org.
  5. [6] . wikidata.org.
  6. [7] . wikidata.org.
  7. [8] . wikidata.org.
  8. [9] . BabelNet. wikidata.org.
  9. [10] . wikidata.org.
  10. [11] . wikidata.org.
  11. [12] . wikidata.org.
  12. [13] . wikidata.org.
  13. [14] . wikidata.org.
  14. [15] . wikidata.org.
  15. [16] . wikidata.org.
  16. [17] . wikidata.org.
  17. [18] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.

Aggregate / graph-position facts

  1. [1] . 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). bialgebra. Retrieved April 10, 2026, from https://4ort.xyz/entity/bialgebra
MLA “bialgebra.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/bialgebra.
BibTeX @misc{4ortxyz_bialgebra_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{bialgebra}}, year = {2026}, url = {https://4ort.xyz/entity/bialgebra}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): bialgebra — https://4ort.xyz/entity/bialgebra (retrieved 2026-04-10)

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