Lie superalgebra
generalization of a Lie algebra with ℤ/2 grading
| rdfs:label |
"Lie superalgebra"@en
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skos:alt |
"super Lie algebra"@en
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| schema:description |
"generalization of a Lie algebra with ℤ/2 grading"@en
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schema:date |
"2026-09-08T12:17:55+00:00"^^xsd:dateTime |
| schema:version | 2542238391 |
| wikibase:identifiers | 14 |
| wikibase:sitelinks | 8 |
| wikibase:statements | 23 |
| p:P10283 | wd:statement/Q1133024-F5D4AEB0-B552-48F3-B551-59688CE43541 |
| p:P10376 | wd:statement/Q1133024-53fa5706-48f2-b976-d09e-bb94ed7e9820 |
| p:P12322 | wd:statement/Q1133024-F3A4DC77-02FA-420D-AF8E-EF1257B12535 |
| p:P13591 | wd:statement/Q1133024-990EC6A6-7DAE-4B51-B306-7ECF3439C608 |
| p:P138 | wd:statement/Q1133024-882971b6-4934-423b-db13-29139f163c0e |
| p:P2163 | wd:statement/Q1133024-F8380947-A071-4B1F-AF71-39AF2A8E2F20 |
| p:P227 | wd:statement/Q1133024-13BFD69C-E865-413E-BF30-C7084FB17B92 |
| p:P244 | wd:statement/Q1133024-6FAF0DD1-BF4F-4639-9B5B-A0427F9C0969 |
| p:P2534 | wd:statement/Q1133024-9e4fcb11-4b88-fd1f-0740-9fba69c409e2 |
| p:P268 | wd:statement/Q1133024-F91C22B8-90B6-4090-88A3-2C9A0093FF31 |
| p:P269 | wd:statement/Q1133024-20C38209-21D8-44F2-9713-8487018C08BB |
| p:P279 | wd:statement/Q1133024-b6ba0067-4ecc-ce64-2113-fccde98da550 |
| p:P3417 | wd:statement/Q1133024-EFD3E77D-B5C6-4DC6-9880-B7EE12310D72 |
| p:P4215 | wd:statement/Q1133024-92622cbd-41ac-c4f2-cb6b-4a62fa91b25e |
| p:P6104 | wd:statement/Q1133024-242BF32B-ACE7-446D-9851-2825E11B35B9 |
| p:P6366 | wd:statement/Q1133024-2830D0AA-3D57-4AED-9C35-A039D8ECDF10 |
| p:P646 | wd:statement/Q1133024-A37F9726-7451-4383-A9E2-28DDFF5B062D |
| p:P7235 | wd:statement/Q1133024-46a28819-4e8e-3b46-0c6a-2eaa25567e20 |
| wd:statement/Q1133024-6c858db5-4151-cb86-6a69-8f0bbb39b46b | |
| wd:statement/Q1133024-b0381fa6-4cb2-8e6f-c107-207b16ced608 | |
| wd:statement/Q1133024-ba7ff3fb-49c8-f0e0-43b4-2de241c4c7b3 | |
| p:P7726 | wd:statement/Q1133024-5a6c791e-4fc5-f728-1be6-f5dec506ecdf |
| p:P8189 | wd:statement/Q1133024-8E4F6C5E-88C3-4D25-AFBD-933F081B2652 |
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p:direct- |
<http:/ |
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p:direct- |
<https:/ |
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p:direct- |
<http:/ |
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p:direct- |
<http:/ |
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p:direct- |
<http:/ |
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p:direct- |
<https:/ |
| wdt:P10283 | "C78804095" |
| wdt:P10376 | "mathematics/lie-superalgebra" |
| wdt:P12322 | super vector space |
| wdt:P13591 | "concept/db6c9349-f744-4705-b2aa-b82f40c9a7ec" |
| wdt:P138 | Sophus Lie |
| wdt:P2163 | "998136" |
| wdt:P227 | "4304027-5" |
| wdt:P244 | "sh94002764" |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow></mtd><mtd><mo stretchy="false">=</mo><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">⊕</mo><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mo stretchy="false">[</mo><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">]</mo></mtd><mtd><mo stretchy="false">⊂</mo><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">+</mo><mi>j</mi><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mo lspace="0.27777777777778em" rspace="0.27777777777778em">mod</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mspace width="0.167em"></mspace></mrow></mrow></mrow></mrow></msub></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo stretchy="false">=</mo><mo stretchy="false">[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">]</mo><mo stretchy="false">+</mo><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mi>x</mi><mo stretchy="false">|</mo><mo stretchy="false">|</mo><mi>y</mi><mo stretchy="false">|</mo></mrow></mrow></msup><mo stretchy="false">[</mo><mi>y</mi><mo>,</mo><mi>x</mi><mo stretchy="false">]</mo></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mi>x</mi><mo stretchy="false">|</mo><mo stretchy="false">|</mo><mi>z</mi><mo stretchy="false">|</mo></mrow></mrow></msup><mo stretchy="false">[</mo><mi>x</mi><mo>,</mo><mo stretchy="false">[</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo stretchy="false">]</mo><mo stretchy="false">]</mo><mo stretchy="false">+</mo><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mi>y</mi><mo stretchy="false">|</mo><mo stretchy="false">|</mo><mi>x</mi><mo stretchy="false">|</mo></mrow></mrow></msup><mo stretchy="false">[</mo><mi>y</mi><mo>,</mo><mo stretchy="false">[</mo><mi>z</mi><mo>,</mo><mi>x</mi><mo stretchy="false">]</mo><mo stretchy="false">]</mo><mo stretchy="false">+</mo><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mi>z</mi><mo stretchy="false">|</mo><mo stretchy="false">|</mo><mi>y</mi><mo stretchy="false">|</mo></mrow></mrow></msup><mo stretchy="false">[</mo><mi>z</mi><mo>,</mo><mo stretchy="false">[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">]</mo><mo stretchy="false">]</mo></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo stretchy="false">=</mo><mo stretchy="false">[</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo stretchy="false">]</mo><mspace width="2em"></mspace><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">∈</mo><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo stretchy="false">=</mo><mo stretchy="false">[</mo><mi>x</mi><mo>,</mo><mo stretchy="false">[</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo stretchy="false">]</mo><mo stretchy="false">]</mo><mspace width="2em"></mspace><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">∈</mo><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P268 | "13191745r" |
| wdt:P269 | "03547128X" |
| wdt:P279 | algebra over a field |
| wdt:P3417 | "Lie-Superalgebra" |
| wdt:P4215 | "super Lie algebra" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "78804095" |
| wdt:P646 | "/m/01rghv" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">[</mo><mo>,</mo><mo stretchy="false">]</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow data-mjx-texclass="ORD"><mi>𝔤</mi></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P7726 | "LieSuperalgebra" |
| wdt:P8189 | "987007534770405171" |
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