@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:-C1KNCBVP-9
  skos:prefLabel "Mautner's lemma"@en, "lemme de Mautner"@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Mautner%27s_lemma> ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-VJSFMZ3M-S, psr:-W9LN9ZRK-5 ;
  dc:created "2023-08-30"^^xsd:date ;
  skos:definition """<b>Mautner's lemma</b> in representation theory, named after Austrian-American mathematician Friederich Mautner, states that if <i>G</i> is a topological group and π a unitary representation of <i>G</i> on a Hilbert space <i>H</i>, then for any <i>x</i> in <i>G</i>, which has conjugates 
<br/>
<br/><dl><dd><i>yxy</i><sup>−1</sup></dd></dl>
<br/>converging to the identity element <i>e</i>, for a net of elements <i>y</i>, then any vector <i>v</i> of <i>H</i> invariant under all the π(<i>y</i>) is also invariant under π(<i>x</i>). 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Mautner%27s_lemma">https://en.wikipedia.org/wiki/Mautner%27s_lemma</a>)"""@en ;
  dc:modified "2023-08-30"^^xsd:date .

psr: a skos:ConceptScheme .
psr:-VJSFMZ3M-S
  skos:prefLabel "topological group"@en, "groupe topologique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-C1KNCBVP-9 .

psr:-W9LN9ZRK-5
  skos:prefLabel "group representation"@en, "représentation de groupe"@fr ;
  a skos:Concept ;
  skos:narrower psr:-C1KNCBVP-9 .