{"id":130895,"date":"1996-01-01T00:00:00","date_gmt":"1996-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/estructuras-de-lie-y-jordan-en-superalgebras-asociativas-con-superinvolucion\/"},"modified":"1996-01-01T00:00:00","modified_gmt":"1996-01-01T00:00:00","slug":"estructuras-de-lie-y-jordan-en-superalgebras-asociativas-con-superinvolucion","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/estructuras-de-lie-y-jordan-en-superalgebras-asociativas-con-superinvolucion\/","title":{"rendered":"Estructuras de lie y jordan en superalgebras asociativas con superinvolucion."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Carlos Gomez Ambrosi <\/strong><\/h2>\n<p>Se desarrolla en la memoria una teoria de herstein (cf.  herstein, rings with involution, chicago univ. Press, 1976) para superalgebras asociativas con superinvolucion, llegando a las siguientes conclusiones.  sea a una superalgebra asociativa simple no trivial unital con superinvolucion * sobre un cuerpo f de caracteristica distinta de 2, y sea z la parte par del centro de a. Llamemos h a la superalgebra de jordan de los elementos simetricos de a con respecto a * y k a la superalgebra de lie de los elementos antisimetricos.  en primer lugar, los resultados siguientes relacionan la simplicidad de a con la estructura de ideales de h, k y k,k .  teorema. H es una superalgebra de jordan simple, salvo que la parte par de a sea conmutativa.  teorema. Si u es un ideal de lie de k entonces u   z o u k,k , salvo que a sea una superalgebra de cuaternios sobre z o la dimension de a sobre z sea 16.  teorema. Si la dimension de a sobre z es mayor que 16 y u es un ideal de lie propio de  k,k  entonces u  z. En particular, si * es de primera clase entonces  k,k  es una superalgebra de lie simple.  por otra parte, el resultado siguiente clasifica los submodulos de la superalgebra a, considerada esta como modulo de jordan sobre h.  teorema. Salvo ciertas excepciones en baja dimension (que se describen completamente en la memoria), los unicos h-submodulos de jordan de a son 0,  h, k y a, donde z. En particular, k es un h-modulo de jordan simple.  finalmente, sin necesidad de suponer ya que a sea simple, se obtiene un resultado sobre extension de homomorfismos de jordan de h en una superalgebra asociativa b a homomorfismos asociativos de a en b.  teorema. Sea   un homomorfismo de jordan de h en una superalgebra asociativa b y supongamos que existen n idempotentes simetricos ortogonales no nulos e1,&#8230;, En en a cuya suma es 1 y tales que aeia = a para todo i = 1,&#8230;,N. Entonces   se extiende univocamente a un homomorfismo asociativo de a<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Estructuras de lie y jordan en superalgebras asociativas con superinvolucion.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Estructuras de lie y jordan en superalgebras asociativas con superinvolucion. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Carlos Gomez Ambrosi <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Zaragoza<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1996<\/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>Santos Gonzalez Jimenez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Sancho De San Roman Juan <\/li>\n<li>Juan Martinez Moreno (vocal)<\/li>\n<li>Michael Racine (vocal)<\/li>\n<li>Juan  Gabriel Tena Ayuso (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Carlos Gomez Ambrosi Se desarrolla en la memoria una teoria de herstein (cf. herstein, rings with involution, [&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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