<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2023000200083</article-id>
<article-id pub-id-type="doi">10.18273/revint.v41n2-2023002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[About Lie algebra classification, conservation laws, and invariant solutions for the relativistic fluid sphere equation]]></article-title>
<article-title xml:lang="es"><![CDATA[Acerca de la clasificación del álgebra de Lie, leyes de conservación y soluciones invariantes para la ecuación de la esfera de fluidos relativista]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[ACEVEDO]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[DUQUE]]></surname>
<given-names><![CDATA[O. M. L.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[HERNÁNDEZ]]></surname>
<given-names><![CDATA[D. A. GARCÍA]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[LOAIZA]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad EAFIT Escuela de Ciencias Aplicadas e Ingenierías ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Faculdad IBMEC  ]]></institution>
<addr-line><![CDATA[Campinas ]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Faculdad IBMEC  ]]></institution>
<addr-line><![CDATA[Campinas ]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad EAFIT Escuela de Ciencias Aplicadas e Ingenierías ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2023</year>
</pub-date>
<volume>41</volume>
<numero>2</numero>
<fpage>83</fpage>
<lpage>101</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2023000200083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2023000200083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2023000200083&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. The optimal generating operators for the relativistic fluid sphere equation have been derived. We have characterized all invariant solutions of this equation using these operators. Furthermore, we have introduced variational symmetries and their corresponding conservation laws, employing both Noether&#8217;s theorem and Ibragimov&#8217;s method. Finally, we have classified the Lie algebra associated with the given equation.  MSC2010: 35A30, 58J70, 76M60.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. Se han derivado los operadores generadores óptimos para la ecua-ción de la esfera de fluido relativista. Hemos caracterizado todas las solucio-nes invariantes de esta ecuación utilizando dichos operadores. Además, hemos introducido simetrías variacionales y sus correspondientes leyes de conserva-ción, empleando tanto el teorema de Noether como el método de Ibragimov. Finalmente, hemos clasificado el álgebra de Lie asociada a la ecuación dada.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Optimal algebra]]></kwd>
<kwd lng="en"><![CDATA[Invariant solutions]]></kwd>
<kwd lng="en"><![CDATA[Lie algebra classification]]></kwd>
<kwd lng="en"><![CDATA[Lie symmetry group]]></kwd>
<kwd lng="en"><![CDATA[Ibragimov&#8217;s method]]></kwd>
<kwd lng="en"><![CDATA[Noether&#8217;s theorem]]></kwd>
<kwd lng="en"><![CDATA[Conservation laws]]></kwd>
<kwd lng="en"><![CDATA[Variational symmetries]]></kwd>
<kwd lng="es"><![CDATA[Álgebra óptima]]></kwd>
<kwd lng="es"><![CDATA[Soluciones invariantes]]></kwd>
<kwd lng="es"><![CDATA[Clasificación de las álgebras de Lie]]></kwd>
<kwd lng="es"><![CDATA[Grupo de simetría de Lie]]></kwd>
<kwd lng="es"><![CDATA[Método de Ibragimov]]></kwd>
<kwd lng="es"><![CDATA[Teorema de Noether]]></kwd>
<kwd lng="es"><![CDATA[Leyes de conservación]]></kwd>
<kwd lng="es"><![CDATA[Simetrías variacionales]]></kwd>
</kwd-group>
</article-meta>
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