@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-KS2JF2N9-4
  skos:prefLabel "nombre complexe déployé"@fr, "split-complex number"@en ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-BV2VH70S-1
  skos:narrower psr:-NGWS6NXB-P, psr:-WLWMB08F-B, psr:-HZ5JWXBQ-C, psr:-LNHFR83L-3, psr:-ZS43QGRB-V, psr:-KS2JF2N9-4, psr:-HM4KTC3M-K, psr:-JKMJN6W0-J, psr:-G912GB3C-D ;
  skos:broader psr:-F1B5QL5S-0, psr:-H31GC9Q4-H ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_composition>, <https://en.wikipedia.org/wiki/Composition_algebra> ;
  skos:definition """In mathematics, a <b>composition algebra</b> <span class="texhtml mvar" style="font-style:italic;">A</span> over a field <span class="texhtml mvar" style="font-style:italic;">K</span> is a not necessarily associative algebra over <span class="texhtml mvar" style="font-style:italic;">K</span> together with a nondegenerate quadratic form  <span class="texhtml mvar" style="font-style:italic;">N</span> that satisfies
         <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle N(xy)=N(x)N(y)}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>N</mi>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mi>y</mi>
         <mo stretchy="false">)</mo>
         <mo>=</mo>
         <mi>N</mi>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mo stretchy="false">)</mo>
         <mi>N</mi>
         <mo stretchy="false">(</mo>
         <mi>y</mi>
         <mo stretchy="false">)</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle N(xy)=N(x)N(y)}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/604c00e2390947f86e0acca312e7fc85f4af2293" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.688ex; height:2.843ex;" alt="N(xy) = N(x)N(y)"></span></dd></dl>
         for all <span class="texhtml mvar" style="font-style:italic;">x</span> and <span class="texhtml mvar" style="font-style:italic;">y</span> in <span class="texhtml mvar" style="font-style:italic;">A</span>.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Composition_algebra">https://en.wikipedia.org/wiki/Composition_algebra</a>)"""@en, """En mathématiques, les algèbres de composition sur un corps commutatif sont des structures algébriques qui généralisent simultanément le corps des nombres complexes, le corps non commutatif des quaternions de Hamilton et l'algèbre des octonions de Cayley. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_composition">https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_composition</a>)"""@fr ;
  skos:prefLabel "composition algebra"@en, "algèbre de composition"@fr ;
  a skos:Concept ;
  dc:modified "2023-08-24"^^xsd:date ;
  dc:created "2023-08-24"^^xsd:date ;
  skos:inScheme psr: .

psr:-NGWS6NXB-P
  skos:prefLabel "octonion"@en, "octonion"@fr ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-LNHFR83L-3
  skos:prefLabel "Petersson algebra"@en, "algèbre de Petersson"@fr ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-WLWMB08F-B
  skos:prefLabel "Okubo algebra"@en, "algèbre d'Okubo"@fr ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-ZS43QGRB-V
  skos:prefLabel "octonion déployé"@fr, "split-octonion"@en ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-F1B5QL5S-0
  skos:prefLabel "algèbre non associative"@fr, "non-associative algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-BV2VH70S-1 .

psr: a skos:ConceptScheme .
psr:-JKMJN6W0-J
  skos:prefLabel "Cayley-Dickson construction"@en, "construction de Cayley-Dickson"@fr ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-HM4KTC3M-K
  skos:prefLabel "nombre multicomplexe"@fr, "multicomplex number"@en ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-H31GC9Q4-H
  skos:prefLabel "quadratic form"@en, "forme quadratique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-BV2VH70S-1 .

psr:-HZ5JWXBQ-C
  skos:prefLabel "algèbre d'octonions"@fr, "octonion algebra"@en ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .

psr:-G912GB3C-D
  skos:prefLabel "quaternion"@fr, "quaternion"@en ;
  a skos:Concept ;
  skos:broader psr:-BV2VH70S-1 .