<?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>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262017000200221</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Calabi-Yau property for graded skew PBW extensions]]></article-title>
<article-title xml:lang="es"><![CDATA[Propiedad Calabi-Yau para extensiones PBW torcidas graduadas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[SUÁREZ]]></surname>
<given-names><![CDATA[HÉCTOR]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[LEZAMA]]></surname>
<given-names><![CDATA[OSWALDO]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[REYES]]></surname>
<given-names><![CDATA[ARMANDO]]></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[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<volume>51</volume>
<numero>2</numero>
<fpage>221</fpage>
<lpage>239</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262017000200221&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262017000200221&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262017000200221&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT. Graded skew PBW extensions were defined by the first author as a generalization of graded iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter regularity and the (skew) Calabi-Yau condition for this kind of extensions. We prove that every graded quasi-commutative skew PBW extension of an Artin-Schelter regular algebra is also an Artin-Schelter regular algebra and, as a consequence, every graded quasi-commutative skew PBW extension of a connected skew Calabi-Yau algebra is skew Calabi-Yau. Finally, we prove that graded skew PBW extensions of a finitely presented connected Auslander-regular algebra are skew Calabi-Yau.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN. Las extensiones PBW torcidas graduadas fueron definidas por el primer autor como una generalización de las extensiones de Ore iteradas graduadas [36]. El propósito de este artículo es estudiar las condiciones Artin-Schelter regular y Calabi-Yau (torcida) para esta clase de extensiones. Demostramos que cada extensión PBW torcida cuasi-conmutativa graduada de un algebra Artin-Schelter regular también es Artin-Schelter regular, y, como consecuencia, que cada extensión PBW torcida cuasi-conmutativa graduada de un álgebra conexa Calabi-Yau torcida es Calabi-Yau torcida. Finalmente, mostramos que las extensiones PBW torcidas graduadas de álgebras Auslander-regular finitamente presentadas y conexas son Calabi-Yau torcidas.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Graded skew PBW extensions]]></kwd>
<kwd lng="en"><![CDATA[AS-regular algebras]]></kwd>
<kwd lng="en"><![CDATA[skew Calabi-Yau algebras]]></kwd>
<kwd lng="es"><![CDATA[Extensiones PBW torcidas graduadas]]></kwd>
<kwd lng="es"><![CDATA[álgebras AS-regular]]></kwd>
<kwd lng="es"><![CDATA[álgebras Calabi-Yau torcidas]]></kwd>
</kwd-group>
</article-meta>
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