{"id":448,"date":"2025-07-17T09:15:31","date_gmt":"2025-07-17T08:15:31","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=448"},"modified":"2025-07-18T09:35:51","modified_gmt":"2025-07-18T08:35:51","slug":"algebres-de-camins-de-leavitt","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/algebres-de-camins-de-leavitt\/","title":{"rendered":"\u00c0lgebres de camins de Leavitt"},"content":{"rendered":"\n<p>\u00c9s ben sabut que per a un cos \\(K\\), l&#8217;isomorfisme \\(K^n\\cong K^m\\) implica que \\(n=m\\). Aquest fet es pot estendre f\u00e0cilment a anells commutatius amb unitat. Quan \\(R\\) no \u00e9s commutatiu, aleshores pot passar que \\(R^n\\cong R^m\\) per\u00f2 \\(n\\neq m\\). Les anomenades \u00e0lgebres de Leavitt modelen aquest comportament. M\u00e9s recentment, les \u00e0lgebres de camins de Leavitt han emergit com una font important d&#8217;exemples que permeten explorar propietats fonamentals en anells i \u00e0lgebres d&#8217;operadors. L&#8217;objectiu del treball \u00e9s entendre el treball fundacional d&#8217;Abrams i Aranda sobre simplicitat i puresa infinita. Si el temps ho permet s&#8217;abordaran casos no simples i la relaci\u00f3 amb C*-\u00e0lgebres.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c9s ben sabut que per a un cos \\(K\\), l&#8217;isomorfisme \\(K^n\\cong K^m\\) implica que \\(n=m\\). Aquest fet es pot estendre f\u00e0cilment a anells commutatius amb unitat. Quan \\(R\\) no \u00e9s commutatiu, aleshores pot passar que \\(R^n\\cong R^m\\) per\u00f2 \\(n\\neq m\\). Les anomenades \u00e0lgebres de Leavitt modelen aquest comportament. M\u00e9s recentment, les \u00e0lgebres de camins de [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,29],"tags":[46],"class_list":["post-448","post","type-post","status-publish","format-standard","hentry","category-algebra","category-analisi-matematica","tag-francesc-perera"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/448","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=448"}],"version-history":[{"count":3,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/448\/revisions"}],"predecessor-version":[{"id":450,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/448\/revisions\/450"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=448"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}