<?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>S0034-74262019000300257</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v53nsupl.84099</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Connes-Landi spheres are homogeneous spaces]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Wilson]]></surname>
<given-names><![CDATA[Mitsuru]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instytut Matematyczny  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Polonia</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>257</fpage>
<lpage>271</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262019000300257&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262019000300257&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262019000300257&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: In this paper, we review some recent developments of compact quantum groups that arise as &#952;-deformations of compact Lie groups of rank at least two. A &#952;-deformation is merely a 2-cocycle deformation using an action of a torus of dimension higher than 2. Using the formula (Lemma 5.3) developed in [11], we derive the noncommutative 7-sphere in the sense of Connes and Landi [3] as the fixed-point subalgebra.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: En este artículo nosotros revisamos algunos desarrollos recientes de grupos cuánticos compactos que surgen en &#952;-deformaciones de grupos compactos de Lie de rango al menos dos. Una &#952;-deformación es simplemente una deformación por 2-cociclo, usando una acción de un toro de dimensión superior a 2. Usando la fórmula (Lemma 5.3) desarrollada en [11], nosotros derivamos la 7-esfera no conmutativa, en el sentido de Connes y Landi [3], como la subálgebra de puntos fijos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Noncommutative geometry]]></kwd>
<kwd lng="en"><![CDATA[quantum homogeneous space]]></kwd>
<kwd lng="en"><![CDATA[compact quantum group]]></kwd>
<kwd lng="en"><![CDATA[Connes-Landi deformation]]></kwd>
<kwd lng="en"><![CDATA[&#952;-deformation]]></kwd>
<kwd lng="es"><![CDATA[Geometría no conmutativa]]></kwd>
<kwd lng="es"><![CDATA[espacio cuántico homogéneo]]></kwd>
<kwd lng="es"><![CDATA[grupo cuántico compacto]]></kwd>
<kwd lng="es"><![CDATA[deformación de Connes-Landi]]></kwd>
<kwd lng="es"><![CDATA[&#952;-deformación]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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