@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:-FBT35M65-C
  skos:prefLabel "algèbre de Lie"@fr, "Lie algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-KFJZXBV9-1 .

psr: a skos:ConceptScheme .
psr:-KFJZXBV9-1
  skos:definition """In mathematics, in particular abstract algebra and topology, a homotopy Lie algebra (or <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 L_{\\\\infty }}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msub>
         <mi>L</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">∞<!-- ∞ --></mi>
         </mrow>
         </msub>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle L_{\\\\infty }}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5ecf05fae003abbd91bc8c749d5a8a807d6efd8" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.458ex; height:2.509ex;" alt="L_{\\\\infty }"></span>-algebra</b>) is a generalisation of the concept of a differential graded Lie algebra. To be a little more specific, the Jacobi identity only holds up to homotopy. Therefore, a differential graded Lie algebra can be seen as a homotopy Lie algebra where the Jacobi identity holds on the nose. These homotopy algebras are useful in classifying deformation problems over characteristic 0 in deformation theory because deformation functors are classified by quasi-isomorphism classes of L∞-algebras. This was later extended to all characteristics by Jonathan Pridham. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Homotopy_Lie_algebra">https://en.wikipedia.org/wiki/Homotopy_Lie_algebra</a>)"""@en ;
  dc:created "2023-08-23"^^xsd:date ;
  dc:modified "2023-08-23"^^xsd:date ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-FBT35M65-C ;
  skos:prefLabel "algèbre de Lie d'homotopie"@fr, "homotopy Lie algebra"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Homotopy_Lie_algebra> .