{"id":55966,"date":"2006-12-12T00:00:00","date_gmt":"2006-12-12T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/teoria-de-representacion-de-coalgebras-localizacion-en-coalgebras\/"},"modified":"2006-12-12T00:00:00","modified_gmt":"2006-12-12T00:00:00","slug":"teoria-de-representacion-de-coalgebras-localizacion-en-coalgebras","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/algebra-homologica\/teoria-de-representacion-de-coalgebras-localizacion-en-coalgebras\/","title":{"rendered":"Teor\u00eda de representaci\u00f3n de co\u00e1lgebras. localizaci\u00f3n en co\u00e1lgebras"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Gabriel Navarro Garulo <\/strong><\/h2>\n<p>El objetivo de la teor\u00eda de representaci\u00f3n de \u00e1lgebras consiste en clasificar \u00e1lgebras, generalmente sobre un cuerpo algebraicamente cerrado, en funci\u00f3n de su categor\u00eda de m\u00f3dulos. Hist\u00f3ricamente los esfuerzos se han centrado en considera \u00fanicamente el caso finito-dimensional. En este sentido destacan los trabajos de gabriel para traducir el problema al contexto de quivers o grafos orientados y de auslander y reiten que proporcionaron unas herramientas fundamental es para el estudio de los m\u00f3dulos de un \u00e1lgebra. Sin embargo, dicha teor\u00eda no es v\u00e1lida si el \u00e1lgebra es de dimensi\u00f3n infinita. A este respecto surge el concepto de co\u00e1lgebra como una generalizaci\u00f3n de las \u00e1lgebras finito-dimensionales y permite una aproximaci\u00f3n al caso general desde el punto de vista cl\u00e1sico.     en la presente tesis doctoral se estudia l posibilidad de un resultado para co\u00e1lgebras an\u00e1logo al conocido teorema de gabriel que describe las \u00e1lgebras b\u00e1sicas finito dimensionales como cocientes de \u00e1lgebras de caminos por un idea admisible. Para este prop\u00f3sito se utilizan la noci\u00f3n de co\u00e1lgebra de caminos de un quiver con relaciones definida por simson. Dado que se obtienen contraejemplos en ese sentido e, incluso, un criterio para decidir cuando una co\u00e1lgebra admisible es la co\u00e1lgebra de caminos de un quiver con relaciones, la clase a considera es reducida a las coalgebras tame. Para tratar este nuevo problema se considera la localizaci\u00f3n en categor\u00edas de comodulos, relacionando la propiedad de ser tame o wild de una co\u00e1lgebra y sus co\u00e1lgebras localizadas. Como consecuencia de dicho an\u00e1lisis se obtiene el siguiente resultado: toda subco\u00e1lgebra admisible tame de una co\u00e1lgebra de caminos de un quiver aciclico es el isomorfa a una co\u00e1lgebra de caminos de un quiver con relaciones.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Teor\u00eda de representaci\u00f3n de co\u00e1lgebras. localizaci\u00f3n en co\u00e1lgebras<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Teor\u00eda de representaci\u00f3n de co\u00e1lgebras. localizaci\u00f3n en co\u00e1lgebras <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Gabriel Navarro Garulo <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Granada<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 12\/12\/2006<\/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>Pascual Jara Mart\u00ednez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Bueso montero Jos\u00e9 Luis <\/li>\n<li>Juan Cuadra d\u00edaz (vocal)<\/li>\n<li>stefaan Caenepell (vocal)<\/li>\n<li>Manuel Saor\u00edn casta\u00f1o (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Gabriel Navarro Garulo El objetivo de la teor\u00eda de representaci\u00f3n de \u00e1lgebras consiste en clasificar \u00e1lgebras, generalmente [&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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