Lie superalgebra (Q2169)
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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)\bmod2}\\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)
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![{\displaystyle [,]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f04349be7aa458edb6f1ab423189a8455c6e21f7)
Identifiers
sh94002764
1 reference
13191745r
1 reference
78804095
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C78804095
1 reference
987007534770405171
mathematics/lie-superalgebra
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super Lie algebra
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LieSuperalgebra
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