{"id":57677,"date":"2018-03-09T22:45:27","date_gmt":"2018-03-09T22:45:27","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/modulos-cruzados-de-algebras-conmutativas-homologa%c2%ada-y-hap\/"},"modified":"2018-03-09T22:45:27","modified_gmt":"2018-03-09T22:45:27","slug":"modulos-cruzados-de-algebras-conmutativas-homologa%c2%ada-y-hap","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/modulos-cruzados-de-algebras-conmutativas-homologa%c2%ada-y-hap\/","title":{"rendered":"M\u00f3dulos cruzados de \u00e1lgebras conmutativas, homolog\u00eda y hap"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Pablo Fern\u00e1ndez Ascariz <\/strong><\/h2>\n<p>En esta tesis se estudia la categor\u00eda de m\u00f3dulos cruzados de \u00e1lgebras conmutativas, la cual generaliza al mismo tiempo dos estructuras diferentes, la de \u00e1lgebra conmutativa y la de m\u00f3dulo. en el primer cap\u00edtulo se dan las nociones b\u00e1sicas y se construyen algunos l\u00edmites. Adem\u00e1s, se muestran varias propiedades de la categor\u00eda, por ejemplo, se prueba que es semiabeliana y tambi\u00e9n que es tripleable (hecho fundamental para poder construir una teor\u00eda de (co)homolog\u00eda), es decir, se da una adjunci\u00f3n entre m\u00f3dulos cruzados y set. A continuaci\u00f3n, se estudia en profundidad el car\u00e1cter no equilibrado de la categor\u00eda y se dan varias definiciones equivalentes a la de m\u00f3dulo cruzado, que ser\u00e1n de gran utilidad para, posteriormente, poder manejar con m\u00e1s facilidad diversos conceptos. en el segundo cap\u00edtulo se definen varias construcciones relacionadas con la categor\u00eda: el actor de un m\u00f3dulo cruzado, los m\u00f3dulos cruzados singulares, el conmutador, el producto tensor, el producto semidirecto, la categor\u00eda de (c,r,f)-m\u00f3dulos y las derivaciones. Adem\u00e1s, se estudian las propiedades de dichos objetos, relacion\u00e1ndolos entre s\u00ed y con sus an\u00e1logos en la categor\u00eda de \u00e1lgebras conmutativas. en el tercer cap\u00edtulo se desarrolla una teor\u00eda de (co)homolog\u00eda de m\u00f3dulos cruzados, y se estudian sus propiedades obteniendo algunos resultados de inter\u00e9s. Tambi\u00e9n se tratan las extensiones de m\u00f3dulos cruzados, se relacionan \u00e9stas con la cohomolog\u00eda definida y se dan dos sucesiones exactas relativas a las diferenciales. Finalmente, se identifica la (co)homolog\u00eda de ciertos m\u00f3dulos cruzados, los m\u00f3dulos cruzados asf\u00e9ricos, con una clase particular de (co)homolog\u00eda relativa de \u00e1lgebras. en el \u00faltimo cap\u00edtulo se hacen c\u00e1lculos efectivos de homolog\u00eda de grupos nilpotentes libres por medio de su \u00e1lgebra de lie asociada. Se observa que este m\u00e9todo es m\u00e1s r\u00e1pido y menos exigente, con respecto a los recursos computacionales que se necesitan, que el que<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>M\u00f3dulos cruzados de \u00e1lgebras conmutativas, homolog\u00eda y hap<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 M\u00f3dulos cruzados de \u00e1lgebras conmutativas, homolog\u00eda y hap <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Pablo Fern\u00e1ndez Ascariz <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Santiago de compostela<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 26\/03\/2007<\/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>Manuel Ladra Gonz\u00e1lez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: emilio Villanueva novoa <\/li>\n<li>j. Ellis graham (vocal)<\/li>\n<li> Hermida alonso Jos\u00e9 \u00e1ngel (vocal)<\/li>\n<li> Ventura alves da silva pedro (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Pablo Fern\u00e1ndez Ascariz En esta tesis se estudia la categor\u00eda de m\u00f3dulos cruzados de \u00e1lgebras conmutativas, 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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2809,4334,126,977],"tags":[2811,38213,127452,71090,127451,127453],"class_list":["post-57677","post","type-post","status-publish","format-standard","hentry","category-algebra","category-algebra-homologica","category-matematicas","category-santiago-de-compostela","tag-emilio-villanueva-novoa","tag-hermida-alonso-jose-angel","tag-j-ellis-graham","tag-manuel-ladra-gonzalez","tag-pablo-fernandez-ascariz","tag-ventura-alves-da-silva-pedro"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/57677","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=57677"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/57677\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=57677"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=57677"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=57677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}