Kac–Moody algebra (Q856666)
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Lie algebra defined by generators and relations through a generalized Cartan matrix
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Kac–Moody algebra |
Lie algebra defined by generators and relations through a generalized Cartan matrix |
Statements
![{\displaystyle {\begin{aligned}C&\in \operatorname {Mat} (n,n;\mathbb {Z} )\\C_{ii}&=2\\C_{ij}&<0\qquad (i\neq 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\neq j)\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb6d85eea8adf170452581db492e7a9d65647053)
0 references
![{\displaystyle [,]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f04349be7aa458edb6f1ab423189a8455c6e21f7)
Identifiers
Sitelinks
Wikipedia(10 entries)
- dewiki Kac-Moody-Algebra
- enwiki Kac–Moody algebra
- fawiki جبر کک-مودی
- frwiki Algèbre de Kac-Moody
- jawiki カッツ・ムーディ代数
- kowiki 카츠-무디 대수
- nlwiki Kac-Moody-algebra
- ptwiki Álgebra de Kac-Moody
- ukwiki Алгебра Каца — Муді
- zhwiki 卡茨-穆迪代数