{"id":83612,"date":"2018-03-10T00:07:47","date_gmt":"2018-03-10T00:07:47","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/grupos-de-braver-y-pa%c2%adcaro-de-coalgebras\/"},"modified":"2018-03-10T00:07:47","modified_gmt":"2018-03-10T00:07:47","slug":"grupos-de-braver-y-pa%c2%adcaro-de-coalgebras","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/grupos-de-braver-y-pa%c2%adcaro-de-coalgebras\/","title":{"rendered":"Grupos de braver y p\u00edcaro de coalgebras"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Juan Cuadra D\u00edaz <\/strong><\/h2>\n<p>En los \u00faltimos a\u00f1os la comunidad matem\u00e1tica ha mostrado un gran inter\u00e9s por la teor\u00eda de co\u00e1lgebras y \u00e1lgebras de hopf debido fundamentalmente a dos razones: por su relaci\u00f3n con la f\u00edsica, y por el gran n\u00famero de areas de las metem\u00e1ticas donde esta estructura aparece, por ejemplo, geometr\u00eda algebraica, teor\u00eda de \u00e1lgebras de lie, teor\u00eda de galois, y combinatoria.  esta tesis se centra en el estudio de la estructura de co\u00e1lgebra desde el punto de vista de la teor\u00eda de invariantes. Es una idea natural en \u00e1lgebra asociar a uan estructura algebraica un objeto m\u00e1s sencillo de estudiar, por ejemplo un grupo, y a trav\u00e9s del estudio de ese objeto deducir propiedades o hacer ciertas clasificaciones de la estructura inicial. Los invariantes analizados en esta tesis son el grupo de baruer y de picard de una co\u00e1lgebra introducidos por b.Torrecillas, f.Van oystaeyen, y y.H. Zhang. Abmos grupos est\u00e1n \u00edntimamente relacionados con la teor\u00eda de equiValencias de categor\u00edas de con m\u00f3dulos, estudiadas por m. Takeuchi y b. I-peng lin. Takeuchi caracteriz\u00f3 las equiValencias entre categor\u00edas de com\u00f3dulos, llamadas hoy dia equiValencias moita-takekuchi, en t\u00e9rminos de los funtores cotensor y co-hom por un cierto bicom\u00f3dulo invertible. Lin estudi\u00f3 las equiValencias entre categor\u00edas de com\u00f3dulos inducidas por equiValencias de morita entre las categor\u00edas de m\u00f3dulos sobre las \u00e1lgebras duales, llamadas equiValencias fuertes.  el contenido de esta tesis se organiza como sigue a continuaci\u00f3n. En el primer cap\u00edtulo se hace un repaso sobre co\u00e1lgebras y \u00e1lgebras de hopf, y se recopilan aquellos resultados b\u00e1sicos de la teor\u00eda necesarios para cap\u00edtulos posteriores. En el cap\u00edtulo 2 se estudia el grupo de picard de una co\u00e1lgebra. Para una co\u00e1lgebra c, el grupo de picard, denotado por pic(c), se puede definir categ\u00f3ricamente como el conjunto de autoequiValencias de la categor\u00eda de com\u00f3dulos mc. Utilizando la caracterizaci\u00f3n da<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Grupos de braver y p\u00edcaro de coalgebras<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Grupos de braver y p\u00edcaro de coalgebras <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Juan Cuadra D\u00edaz <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Almer\u00eda<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 29\/02\/2000<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Blas Torrecillas Jover<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  G\u00f3mez pardo Jos\u00e9 Luis <\/li>\n<li> Del ri\u00f3 mateos \u00e1ngel (vocal)<\/li>\n<li>freddy Van ovstaneyen (vocal)<\/li>\n<li>Jos\u00e9 G\u00f3mez torecillas (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Juan Cuadra D\u00edaz En los \u00faltimos a\u00f1os la comunidad matem\u00e1tica ha mostrado un gran inter\u00e9s por la [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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