<?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>S0034-74262019000300001</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v53nsupl.83958</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Pointed Hopf algebras: a guided tour to the liftings]]></article-title>
<article-title xml:lang="es"><![CDATA[Álgebras de Hopf punteadas: una excursión a los levantamientos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Angiono]]></surname>
<given-names><![CDATA[Iván]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García Iglesias]]></surname>
<given-names><![CDATA[Agustín]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Córdoba  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional de Córdoba  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Argentina</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<volume>53</volume>
<fpage>1</fpage>
<lpage>44</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262019000300001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262019000300001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262019000300001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: This article serves a two-fold purpose. On the one hand, it is a survey about the classi cation of finite-dimensional pointed Hopf algebras with abelian coradical, whose final step is the computation of the liftings or deformations of graded Hopf algebras. On the other, we present a step-by-step guide to carry out the strategy developed to construct the liftings. As an example, we conclude the work with the classification of pointed Hopf algebras of Cartan type B 2.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Este artículo tiene un doble propósito. Por un lado, repasamos la clasificación de las álgebras de Hopf punteadas de dimensión finita con corradical abeliano, cuyo paso final es el cálculo de los levantamientos o deformaciones de álgebras de Hopf graduadas. Por otro, presentamos una guía paso a paso para llevar a cabo la estrategia desarrollada para construir los levantamientos. Concluimos el trabajo con un ejemplo donde damos la clasificación de las álgebras de Hopf punteadas de tipo Cartan B 2.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Hopf algebras]]></kwd>
<kwd lng="en"><![CDATA[Liftings]]></kwd>
<kwd lng="en"><![CDATA[Cleft objetcs]]></kwd>
<kwd lng="es"><![CDATA[Álgebras de Hopf]]></kwd>
<kwd lng="es"><![CDATA[Levantamientos]]></kwd>
<kwd lng="es"><![CDATA[Objetos hendidos]]></kwd>
</kwd-group>
</article-meta>
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<ref id="B30">
<label>[30]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schauenburg]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hopf bi-Galois extensions]]></article-title>
<source><![CDATA[Comm. Algebra]]></source>
<year>1996</year>
<volume>24</volume>
<page-range>3797-825</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
