{"id":666,"date":"2015-05-31T11:25:46","date_gmt":"2015-05-31T19:25:46","guid":{"rendered":"http:\/\/www.garibaldibros.com\/wp\/?p=666"},"modified":"2015-06-09T13:10:54","modified_gmt":"2015-06-09T21:10:54","slug":"new-preprint-on-outer-automorphisms-of-simple-groups","status":"publish","type":"post","link":"https:\/\/www.garibaldibros.com\/wp\/new-preprint-on-outer-automorphisms-of-simple-groups\/","title":{"rendered":"New preprint on outer automorphisms of simple groups"},"content":{"rendered":"

New preprint out today:\u00a0Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras<\/a>, written\u00a0with Holger P. Petersson<\/a>. \u00a0In it, we study the question of existence of outer automorphisms of simple algebraic groups. \u00a0One knows that the *-action and the Tits class provide obstructions to the existence of outer automorphisms, and the question is whether they are the only obstruction. \u00a0That is, if the obstructions vanish, does there necessarily exist a corresponding outer automorphism, equivalently, a rational point on the corresponding non-identity component of the automorphism group (viewed as a variety)? \u00a0For semisimple groups, the answer is easily seen to be “no”, but for simple groups so far the answer is “yes” in all cases where we know it. \u00a0There were\u00a0four remaining classes of simple groups for which the answer was unknown, and one of our main results is to settle one of those four cases, the trialitarian groups.<\/p>\n","protected":false},"excerpt":{"rendered":"

New preprint out today:\u00a0Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras, written\u00a0with Holger P. Petersson. \u00a0In it, we study the question of existence of outer automorphisms of simple algebraic groups. \u00a0One knows that the *-action and the Tits class provide obstructions to the existence of outer automorphisms, and the question is…<\/p>\n","protected":false},"author":1,"featured_media":677,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,7],"tags":[],"class_list":["post-666","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-algebra","category-papers"],"yoast_head":"\nNew preprint on outer automorphisms of simple groups - Skip Garibaldi<\/title>\n<meta name=\"description\" content=\"Preprint on outer automorphisms of simple groups\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.garibaldibros.com\/wp\/new-preprint-on-outer-automorphisms-of-simple-groups\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"New preprint on outer automorphisms of simple groups - Skip Garibaldi\" \/>\n<meta property=\"og:description\" content=\"Preprint on outer automorphisms of simple groups\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.garibaldibros.com\/wp\/new-preprint-on-outer-automorphisms-of-simple-groups\/\" \/>\n<meta property=\"og:site_name\" content=\"Skip Garibaldi\" \/>\n<meta property=\"article:published_time\" content=\"2015-05-31T19:25:46+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2015-06-09T21:10:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.garibaldibros.com\/wp\/wp-content\/uploads\/2015\/05\/Buekenhout_Triality.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1650\" \/>\n\t<meta property=\"og:image:height\" content=\"1275\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Skip Garibaldi\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@skipgaribaldi\" \/>\n<meta name=\"twitter:site\" content=\"@skipgaribaldi\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Skip Garibaldi\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/new-preprint-on-outer-automorphisms-of-simple-groups\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/new-preprint-on-outer-automorphisms-of-simple-groups\\\/\"},\"author\":{\"name\":\"Skip Garibaldi\",\"@id\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/#\\\/schema\\\/person\\\/6b3bb7d9b4cf0fde5aed4ab52133ce07\"},\"headline\":\"New preprint on outer automorphisms of simple groups\",\"datePublished\":\"2015-05-31T19:25:46+00:00\",\"dateModified\":\"2015-06-09T21:10:54+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/new-preprint-on-outer-automorphisms-of-simple-groups\\\/\"},\"wordCount\":161,\"publisher\":{\"@id\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/#\\\/schema\\\/person\\\/6b3bb7d9b4cf0fde5aed4ab52133ce07\"},\"image\":{\"@id\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/new-preprint-on-outer-automorphisms-of-simple-groups\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/wp-content\\\/uploads\\\/2015\\\/05\\\/Buekenhout_Triality.png\",\"articleSection\":[\"algebra\",\"papers\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/new-preprint-on-outer-automorphisms-of-simple-groups\\\/\",\"url\":\"https:\\\/\\\/www.garibaldibros.com\\\/wp\\\/new-preprint-on-outer-automorphisms-of-simple-groups\\\/\",\"name\":\"New preprint on outer automorphisms of simple groups - 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