Kac–Moody algebra
Lie algebra defined by generators and relations through a generalized Cartan matrix
Facts
6 properties- Subclass of
- generalized Kac–Moody algebra[4]
- Defining formula
- \begin{aligned}C&\in\operatorname{Mat}(n,n;\mathbb Z)\\C_{ii}&=2\\C_{ij}&<0\qquad(i\ne j)\\C_{ij}=0&\iff C_{ji}&=0\\{}[h_i,h_j]&=0\\{}[h_i,e_j]&=C_{ij}e_j\\{}[h_i,f_j]&=-C_{ij}f_j\\{}[e_i,f_j]&=\delta_{ij}h_i\\\operatorname{ad}(e_i)^{1-C_{ij}}(e_j)&=\operatorname{ad}(f_i)^{1-C_{ij}}(f_j)=0\qquad(i\ne j)\end{aligned}
- Discoverer or inventor
- Victor Kac[1]
- In defining formula
- C, [,], \operatorname{ad}, \delta
- Maintained by WikiProject
- WikiProject Mathematics[5]
- Named after
- Victor Kac, Robert Moody[2][3]
🏷️ Also known as
en Kac–Moody algebra
de Kac-Moody-Algebra
es álgebra de Kac-Moody
fa جبر کک-مودی
fr algèbre de Kac-Moody
ja カッツ・ムーディ代数
ko 카츠-무디 대수
ru алгебра Каца — Муди
tr Kac-Moody cebiri
uk Алгебра Каца — Муді
zh Kac-Moody代数
zh Kac-Moody代數
zh 卡克-穆迪代数
zh 卡茨-穆迪代数
zh-hant 卡茨-穆迪代數
🔖 Identifiers · 14
- Library of Congress Authorities ID
- sh89002479
- GND ID
- 4223399-9
- OpenAlex ID
- C29945619
- Bibliothèque nationale de France ID
- 12126021f
- Encyclopedia of Mathematics article ID
- Kac-Moody_algebra
- FAST ID
- 985623
- Freebase ID
- /m/04b8zm
- IdRef ID
- 029690005
- J9U entity ID
- 987007546306105171
- Microsoft Academic ID (discontinued)
- 29945619
- NLab ID
- Kac-Moody algebra
- ScienceDirect topic ID
- mathematics/kac-moody-algebra
Show all 14 identifiers +2
- Stack Exchange tag
- mathoverflow.net, math.stackexchange.com
- Yale LUX ID
- concept/22b09ecd-df91-4164-8278-9877af47efc2
🔗 Connections
Named after 2
Subtypes 2
Created notable works 1
Discoverer or inventor 1
Maintained by WikiProject 1
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