<?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>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2020000400418</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.66.418</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Double and dual numbers. SU(2) groups, two-component spinors and generating functions]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Torres del Castillo]]></surname>
<given-names><![CDATA[G.F.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gutiérrez-Herrera]]></surname>
<given-names><![CDATA[K.C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Puebla Instituto de Ciencias ]]></institution>
<addr-line><![CDATA[Puebla Pue.]]></addr-line>
<country>México</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Puebla Facultad de Ciencias Físico Matemáticas ]]></institution>
<addr-line><![CDATA[Puebla Pue.]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>08</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>08</month>
<year>2020</year>
</pub-date>
<volume>66</volume>
<numero>4</numero>
<fpage>418</fpage>
<lpage>423</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2020000400418&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2020000400418&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2020000400418&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We explicitly show that the groups of  2 × 2 unitary matrices with determinant equal to 1 whose entries are double or dual numbers are homomorphic to ${\rm SO}(2,1)$ or to the group of rigid motions of the Euclidean plane, respectively, and we introduce the corresponding two-component spinors. We show that with the aid of the double numbers we can find generating functions for separable solutions of the Laplace equation in the  ( 2 + 1 ) Minkowski space, which contain special functions that also appear in the solution of the Laplace equation in the three-dimensional Euclidean space, in spheroidal and toroidal coordinates.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Mostramos explícitamente que los grupos de matrices unitarias  2 × 2 con determinante igual a 1 cuyas entradas son números dobles o números duales son homomorfos a ${\rm SO}(2,1)$ o al grupo de movimientos rígidos del plano euclideano, respectivamente, e introducimos los espinores de dos componentes correspondientes. Mostramos que con la ayuda de los números dobles podemos hallar funciones generatrices para soluciones separables de la ecuación de Laplace en el espacio de Minkowski  ( 2 + 1 ), las cuales contienen funciones especiales que también aparecen en la solución de la ecuación de Laplace en el espacio euclideano tridimensional, en coordenadas esferoidales y toroidales.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Double numbers]]></kwd>
<kwd lng="en"><![CDATA[dual numbers]]></kwd>
<kwd lng="en"><![CDATA[unitary groups]]></kwd>
<kwd lng="en"><![CDATA[spinors]]></kwd>
<kwd lng="en"><![CDATA[Minkowski (2 + 1) space]]></kwd>
<kwd lng="en"><![CDATA[Laplace&#8217;s equation]]></kwd>
<kwd lng="en"><![CDATA[spheroidal coordinates]]></kwd>
<kwd lng="en"><![CDATA[toroidal coordinates]]></kwd>
<kwd lng="es"><![CDATA[Números dobles]]></kwd>
<kwd lng="es"><![CDATA[números duales]]></kwd>
<kwd lng="es"><![CDATA[grupos unitarios]]></kwd>
<kwd lng="es"><![CDATA[espinores]]></kwd>
<kwd lng="es"><![CDATA[espacio de Minkowski (2 + 1)]]></kwd>
<kwd lng="es"><![CDATA[ecuación de Laplace]]></kwd>
<kwd lng="es"><![CDATA[coordenadas esferoidales]]></kwd>
<kwd lng="es"><![CDATA[coordenadas toroidales]]></kwd>
</kwd-group>
</article-meta>
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