@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:-LLND57KL-D
  skos:prefLabel "algèbre associative"@fr, "associative algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-XP5BM1D2-V .

psr:-DWGDCN0G-R
  skos:prefLabel "operator algebra"@en, "algèbre d'opérateurs"@fr ;
  a skos:Concept ;
  skos:narrower psr:-XP5BM1D2-V .

psr:-XP5BM1D2-V
  skos:broader psr:-RXQC777M-K, psr:-RRBN6FVB-9, psr:-DWGDCN0G-R, psr:-LLND57KL-D ;
  skos:prefLabel "algèbre de Weyl"@fr, "Weyl algebra"@en ;
  skos:definition """In abstract algebra, the <b>Weyl algebra</b> is the ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form
<br/>
<br/><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 f_{m}(X)\\\\partial _{X}^{m}+f_{m-1}(X)\\\\partial _{X}^{m-1}+\\\\cdots +f_{1}(X)\\\\partial _{X}+f_{0}(X).}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>f</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>X</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <msubsup>
<br/>          <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>X</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>f</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>X</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <msubsup>
<br/>          <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>X</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mo>+</mo>
<br/>        <mo>⋯<!-- ⋯ --></mo>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>f</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>X</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <msub>
<br/>          <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>X</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>f</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>X</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle f_{m}(X)\\\\partial _{X}^{m}+f_{m-1}(X)\\\\partial _{X}^{m-1}+\\\\cdots +f_{1}(X)\\\\partial _{X}+f_{0}(X).}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3ec0d47be6129f0ba7e703895a1320590ea4682" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:53.009ex; height:3.343ex;" alt="{\\\\displaystyle f_{m}(X)\\\\partial _{X}^{m}+f_{m-1}(X)\\\\partial _{X}^{m-1}+\\\\cdots +f_{1}(X)\\\\partial _{X}+f_{0}(X).}"></span></dd></dl>
<br/>More precisely, let <i>F</i> be the underlying field, and let <i>F</i>[<i>X</i>] be the ring of polynomials in one variable, <i>X</i>, with coefficients in <i>F</i>.  Then each <i>f<sub>i</sub></i> lies in <i>F</i>[<i>X</i>].
<br/><i>∂<sub>X</sub></i> is the derivative with respect to <i>X</i>.  The algebra is generated by <i>X</i> and <i>∂<sub>X</sub></i>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Weyl_algebra">https://en.wikipedia.org/wiki/Weyl_algebra</a>)"""@en, """En mathématiques, et plus précisément en algèbre générale, l'algèbre de Weyl est un anneau d'opérateurs différentiels dont les coefficients sont des polynômes à une variable. Cette algèbre (et d'autres la généralisant, appelées elles aussi algèbres de Weyl) a été introduite par Hermann Weyl en 1928 comme outil d'étude du principe d'incertitude en mécanique quantique. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Weyl">https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Weyl</a>)"""@fr ;
  dc:created "2023-08-04"^^xsd:date ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Weyl_algebra>, <https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Weyl> ;
  skos:inScheme psr: ;
  a skos:Concept ;
  dc:modified "2023-08-23"^^xsd:date .

psr:-RXQC777M-K
  skos:prefLabel "algèbre différentielle"@fr, "differential algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-XP5BM1D2-V .

psr: a skos:ConceptScheme .
psr:-RRBN6FVB-9
  skos:prefLabel "opérateur différentiel"@fr, "differential operator"@en ;
  a skos:Concept ;
  skos:narrower psr:-XP5BM1D2-V .