@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:-DG57JJ6T-P
  skos:prefLabel "algèbre de Jordan"@fr, "Jordan algebra"@en ;
  skos:narrower psr:-G0MHL2B4-5 ;
  a skos:Concept ;
  dc:modified "2023-08-24"^^xsd:date ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Jordan_algebra>, <https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Jordan> ;
  skos:definition """In abstract algebra, a <b>Jordan algebra</b> is a nonassociative algebra over a field whose multiplication satisfies the following axioms:
         
         <ol><li><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 xy=yx}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>x</mi>
         <mi>y</mi>
         <mo>=</mo>
         <mi>y</mi>
         <mi>x</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle xy=yx}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2b203fa309e89fccdbba22909c8418f6b229779" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.069ex; height:2.009ex;" alt="xy=yx"></span> (commutative law)</li>
         <li><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 (xy)(xx)=x(y(xx))}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mi>y</mi>
         <mo stretchy="false">)</mo>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mi>x</mi>
         <mo stretchy="false">)</mo>
         <mo>=</mo>
         <mi>x</mi>
         <mo stretchy="false">(</mo>
         <mi>y</mi>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mi>x</mi>
         <mo stretchy="false">)</mo>
         <mo stretchy="false">)</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle (xy)(xx)=x(y(xx))}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdcded1ca6f96c8d6e946cc48e4c0af32d2cd916" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.625ex; height:2.843ex;" alt="(xy)(xx)=x(y(xx))"></span> (<style data-mw-deduplicate="TemplateStyles:r1023754711">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}</style><span class="vanchor"><span id="Jordan_identity"></span><span class="vanchor-text">Jordan identity</span></span>).</li></ol>
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Jordan_algebra">https://en.wikipedia.org/wiki/Jordan_algebra</a>)"""@en, """En algèbre générale, une algèbre de Jordan est une algèbre sur un corps commutatif, dans laquelle l'opération de multiplication interne, <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 (x,y)\\
ightarrow (x\\\\cdot y)}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mo>,</mo>
         <mi>y</mi>
         <mo stretchy="false">)</mo>
         <mo stretchy="false">→<!-- → --></mo>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mi>y</mi>
         <mo stretchy="false">)</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle (x,y)\\
ightarrow (x\\\\cdot y)}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edd95345282093c2cc21ea5a5eaab76477d80078" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.916ex; height:2.843ex;" alt="(x,y)\\
ightarrow (x\\\\cdot y)"></span> a deux propriétés : 
         <ul><li>elle est commutative, c’est-à-dire que <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 x\\\\cdot y=y\\\\cdot x,}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>x</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mi>y</mi>
         <mo>=</mo>
         <mi>y</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mi>x</mi>
         <mo>,</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle x\\\\cdot y=y\\\\cdot x,}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a85800340ce861cfb17c12c8df690e737170089" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.074ex; height:2.009ex;" alt="x\\\\cdot y=y\\\\cdot x,"></span></li>
         <li>elle vérifie l'identité suivante, dite <b>identité de Jordan</b> : <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 (x\\\\cdot y)\\\\cdot (x\\\\cdot x)=x\\\\cdot (y\\\\cdot (x\\\\cdot x))}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mi>y</mi>
         <mo stretchy="false">)</mo>
         <mo>⋅<!-- ⋅ --></mo>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mi>x</mi>
         <mo stretchy="false">)</mo>
         <mo>=</mo>
         <mi>x</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mo stretchy="false">(</mo>
         <mi>y</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mo stretchy="false">(</mo>
         <mi>x</mi>
         <mo>⋅<!-- ⋅ --></mo>
         <mi>x</mi>
         <mo stretchy="false">)</mo>
         <mo stretchy="false">)</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle (x\\\\cdot y)\\\\cdot (x\\\\cdot x)=x\\\\cdot (y\\\\cdot (x\\\\cdot x))}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c14d3576c67928e052895fe9d80a717795d0c0a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.699ex; height:2.843ex;" alt="(x\\\\cdot y)\\\\cdot (x\\\\cdot x)=x\\\\cdot (y\\\\cdot (x\\\\cdot x))"></span>.</li></ul>
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Jordan">https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Jordan</a>)"""@fr ;
  skos:inScheme psr: ;
  skos:broader psr:-F1B5QL5S-0, psr:-QDSZ76FR-B .

psr:-QDSZ76FR-B
  skos:prefLabel "quantum field theory"@en, "théorie quantique des champs"@fr ;
  a skos:Concept ;
  skos:narrower psr:-DG57JJ6T-P .

psr:-F1B5QL5S-0
  skos:prefLabel "algèbre non associative"@fr, "non-associative algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-DG57JJ6T-P .

psr: a skos:ConceptScheme .
psr:-G0MHL2B4-5
  skos:prefLabel "algèbre d'Albert"@fr, "Albert algebra"@en ;
  a skos:Concept ;
  skos:broader psr:-DG57JJ6T-P .