pre-Lie algebra
possibly non-associative algebra in which the associator is invariant under the exchange of the two latter arguments, which implies that the commutator obeys the Jacobi identity
| rdfs:label |
"pre-Lie algebra"@en
|
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skos:alt |
"Koszul-Vinberg algebra"@en
"Vinberg algebra"@en
"left-symmetric algebra"@en
"right-symmetric algebra"@en
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| schema:description |
"possibly non-associative algebra in which the associator is invariant under the exchange of the two latter arguments, which implies that the commutator obeys the Jacobi identity"@en
|
|
schema:date |
"2026-09-08T12:41:33+00:00"^^xsd:dateTime |
| schema:version | 2542248382 |
| wikibase:identifiers | 3 |
| wikibase:sitelinks | 3 |
| wikibase:statements | 6 |
| p:P2534 | wd:statement/Q7239170-ccf3f51c-48ea-5525-8609-32d0d5617086 |
| p:P279 | wd:statement/Q7239170-34ca32cb-4a7e-a9a1-771f-5fb92ba8d9ae |
| p:P4215 | wd:statement/Q7239170-935D5AFD-0B6B-4E5B-BFB3-AC7FC0B10215 |
| p:P6366 | wd:statement/Q7239170-6EC6E251-23D1-4768-9F7A-00532F3FF05E |
| p:P646 | wd:statement/Q7239170-73F31D2D-1ADD-49AD-B93D-418C3C56584A |
| p:P7235 | wd:statement/Q7239170-f99004b5-40df-1678-fae9-587add647746 |
|
p:direct- |
<https:/ |
| 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"><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">◃</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">◃</mo><mi>z</mi><mo stretchy="false">−</mo><mi>x</mi><mo stretchy="false">◃</mo><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">◃</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">◃</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">◃</mo><mi>y</mi><mo stretchy="false">−</mo><mi>x</mi><mo stretchy="false">◃</mo><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">◃</mo><mi>y</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P279 | algebra over a field |
| wdt:P4215 | "pre-Lie algebra" |
| wdt:P6366 | "2780419923" |
| wdt:P646 | "/m/0gfjm6w" |
| 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><mi>x</mi><mo stretchy="false">◃</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">◃</mo><mi>z</mi><mo stretchy="false">−</mo><mi>x</mi><mo stretchy="false">◃</mo><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">◃</mo><mi>z</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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