Lie superalgebra (Q1133024)
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generalization of a Lie algebra with ℤ/2 grading
- super Lie algebra
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lie superalgebra |
generalization of a Lie algebra with ℤ/2 grading |
|
Statements
![{\displaystyle {\begin{aligned}{\mathfrak {g}}&={\mathfrak {g}}_{0}\oplus {\mathfrak {g}}_{1}\\{}[{\mathfrak {g}}_{i},{\mathfrak {g}}_{j}]&\subset {\mathfrak {g}}_{(i+j){\bmod {2}}}\\0&=[x,y]+(-1)^{|x||y|}[y,x]\\0&=(-1)^{|x||z|}[x,[y,z]]+(-1)^{|y||x|}[y,[z,x]]+(-1)^{|z||y|}[z,[x,y]]\\0&=[x,x]\qquad (x\in {\mathfrak {g}}_{0})\\0&=[x,[x,x]]\qquad (x\in {\mathfrak {g}}_{1})\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c559ea90f8ab6bfe6987d25d3920ea5ba3b02bb7)
0 references
![{\displaystyle [,]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f04349be7aa458edb6f1ab423189a8455c6e21f7)
Identifiers
1 reference
1 reference
Sitelinks
Wikipedia(8 entries)
- cawiki Super àlgebra de Lie
- enwiki Lie superalgebra
- eswiki Super álgebra de Lie
- frwiki Superalgèbre de Lie
- itwiki Superalgebra di Lie
- kowiki 리 초대수
- ptwiki Superalgebra Lie
- zhwiki 李超代数