<?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>1794-9165</journal-id>
<journal-title><![CDATA[Ingeniería y Ciencia]]></journal-title>
<abbrev-journal-title><![CDATA[ing.cienc.]]></abbrev-journal-title>
<issn>1794-9165</issn>
<publisher>
<publisher-name><![CDATA[Escuela de Ciencias y Humanidades y Escuela de Ingeniería de la Universidad EAFIT]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1794-91652018000100029</article-id>
<article-id pub-id-type="doi">10.17230/ingciencia.14.27.2</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Symmetry and Reversibility Properties for Quantum Algebras and Skew Poincaré Birkhoff-Witt Extensions]]></article-title>
<article-title xml:lang="es"><![CDATA[Propiedades de simetría y reversibilidad para álgebras cuánticas y extensiones torcidas de Poincaré-Birkhoff-Witt]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Reyes]]></surname>
<given-names><![CDATA[Armando]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jaramillo]]></surname>
<given-names><![CDATA[Julio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Orinoquia ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>14</volume>
<numero>27</numero>
<fpage>29</fpage>
<lpage>52</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1794-91652018000100029&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1794-91652018000100029&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1794-91652018000100029&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Our aim in this paper is to investigate symmetry and reversibility properties for quantum algebras and skew PBW extensions. Under certain conditions we prove that these properties transfer from a ring of coefficients to a quantum algebra or skew PBW extension over this ring. In this way we generalize several results established in the literature and consider algebras which have not been studied before. We illustrate our results with remarkable examples of theoretical physics.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Nuestro propósito en este artículo es investigar las propiedades de simetría y reversibilidad para álgebras cuánticas y extensiones PBW torcidas. Bajo ciertas condiciones mostramos que estas propiedades se transfieren de un anillo de coeficientes a un álgebra cuántica o extensión PBW torcida sobre este anillo. De esta manera generalizamos diversos resultados establecidos en la literatura, y los ampliamos a álgebras antes no estudiadas. Ilustramos nuestros resultados con ejemplos destacados de la física teórica.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Symmetry]]></kwd>
<kwd lng="en"><![CDATA[reversibility]]></kwd>
<kwd lng="en"><![CDATA[quantum algebra]]></kwd>
<kwd lng="en"><![CDATA[skew Poincaré-Birkhoff-Witt extension]]></kwd>
<kwd lng="es"><![CDATA[Simetría]]></kwd>
<kwd lng="es"><![CDATA[reversibilidad]]></kwd>
<kwd lng="es"><![CDATA[álgebra cuántica]]></kwd>
<kwd lng="es"><![CDATA[extensión torcida de Poincaré-Birkhoff-Witt]]></kwd>
</kwd-group>
</article-meta>
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