{"id":6216,"date":"2023-08-29T14:00:23","date_gmt":"2023-08-29T21:00:23","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=6216"},"modified":"2025-02-13T12:16:54","modified_gmt":"2025-02-13T19:16:54","slug":"added-visualization-of-the-embeddings-of-the-maximal-subgroups-with-associated-projection-matrices-of-lie-algebras-in-the-dynkin-diagram-pane-4-of-visiblie_e8","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2023\/08\/29\/added-visualization-of-the-embeddings-of-the-maximal-subgroups-with-associated-projection-matrices-of-lie-algebras-in-the-dynkin-diagram-pane-4-of-visiblie_e8\/","title":{"rendered":"Added visualization of the embeddings of the maximal subgroups with associated projection matrices of Lie Algebras in the Dynkin Diagram pane (#4) of VisibLie_E8"},"content":{"rendered":"\n<p>This is constructed from&nbsp;<a href=\"https:\/\/theoryofeverything.org\/theToE\/visualizations\/interactive\/\">VisibLie_E8<\/a>&nbsp; and uses the Mathematica package&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2011.01764\">Mathgroup<\/a>. A comprehensive PowerPoint\/PDF that gives an overview of the underlying theory and VisibLie_E8 tool capability is in <a href=\"https:\/\/theoryofeverything.org\/theToE\/2023\/02\/17\/quaternion-weyl-orbits-from-coxeter-dynkin-geometric-group-theory\/\" target=\"_blank\" rel=\"noopener\" title=\"\">this post<\/a>. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2023\/09\/new-dynkin-ppt-2.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"4918\" height=\"3888\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2023\/09\/new-dynkin-ppt-2.png\" alt=\"\" class=\"wp-image-6225\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2023\/09\/E8MaximalEmbeddings-2.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"6378\" height=\"14947\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2023\/09\/E8MaximalEmbeddings-2.png\" alt=\"\" class=\"wp-image-6222\"\/><\/a><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is constructed from&nbsp;VisibLie_E8&nbsp; and uses the Mathematica package&nbsp;Mathgroup. A comprehensive PowerPoint\/PDF that gives an overview of the underlying theory and VisibLie_E8 tool capability is in this post.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[4,14,5],"class_list":["post-6216","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-math","tag-toe"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=6216"}],"version-history":[{"count":11,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6216\/revisions"}],"predecessor-version":[{"id":6886,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6216\/revisions\/6886"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=6216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=6216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=6216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}