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affine Lie algebra

central extension of the Lie algebra of Laurent polynomials valued in a simple Lie algebra
Class type of: Kac–Moody algebra Q632521
affine Lie algebra
self · Public Domain · Wikimedia

Facts

3 properties
Subclass of
Kac–Moody algebra
Defining formula
\begin{aligned}&\hat{\mathfrak g}=\mathfrak g\otimes \mathbb C[t,t^{-1}]\oplus\mathbb Cc\\&[a\otimes t^{n}+\alpha c,b\otimes t^m+\beta c]=[a,b]\otimes t^{n+m}+\langle a|b\rangle n\delta_{m+n,0}c\end{aligned}
In defining formula
\hat{\mathfrak g}, \mathfrak g, \mathbb C[t,t^{-1}], c, \langle~|~\rangle, \delta
🏷️ Also known as
en affine Lie algebra de affine Lie-Algebra fa جبر لی آفین fr algèbre de Lie affine ja アフィンリー代数 ko 아핀 리 대수 ko 아핀 카츠-무디 대수 pt álgebra de Lie afim ru аффинная алгебра Ли uk афінна алгебра Лі zh 仿射李代数 zh 仿射李代數
🔖 Identifiers · 9
GND ID
4141571-1
OpenAlex ID
C5475112
Freebase ID
/m/04vx9_
Gran Enciclopèdia Catalana ID
algebra-de-lie-0
Gran Enciclopèdia Catalana ID (former scheme)
0267692
Microsoft Academic ID (discontinued)
5475112
NLab ID
affine Lie algebra
ScienceDirect topic ID
mathematics/affine-lie-algebra, mathematics/affine-kac
Stack Exchange tag
physics.stackexchange.com

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🔗 Connections
Subclass of 1
Kac–Moody algebra
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Summary

affine Lie algebra is a type of Kac–Moody algebra[1].

References

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Direct Wikidata claims

  1. [1] ↑ . wikidata.org.

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APA 4ort.xyz Knowledge Graph. (2026). affine Lie algebra. Retrieved November 11, 2026, from https://4ort.xyz/entity/affine-lie-algebra
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BibTeX @misc{4ortxyz_affine-lie-algebra_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{affine Lie algebra}}, year = {2026}, url = {https://4ort.xyz/entity/affine-lie-algebra}, note = {Accessed: 2026-11-11}}
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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. 17w ago · Charp238 · 2026-07-11 view diff on Wikidata ↗
    Defining formula → \begin{aligned}&\hat{\mathfrak g}=\mathfrak g\otimes \mathbb
    Subclass of → Kac–Moody algebra
    "Created claim: Defining formula: \begin{aligned}\hat{\mathfrak g}&=\mathfrak g\otimes \mathbb C[t,t^{-1}]\oplus\mathbb Cc\\{}[a\otimes t^{n}+\alpha c,b\otimes t^m+\beta c]=[a,b]\otimes"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.