{"id":1356,"date":"2013-08-10T07:25:05","date_gmt":"2013-08-10T14:25:05","guid":{"rendered":"http:\/\/theoryofeverything.org\/MyToE\/?p=1356"},"modified":"2013-08-10T07:25:05","modified_gmt":"2013-08-10T14:25:05","slug":"hyperbolic-dynkin-diagrams","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2013\/08\/10\/hyperbolic-dynkin-diagrams\/","title":{"rendered":"Hyperbolic Dynkin Diagrams"},"content":{"rendered":"<p>I am pleased to announce the availability of the comprehensive set of 238 Hyperbolic Dynkin diagrams ranks 3 to 10. These are enumerated <a href=\"http:\/\/arxiv.org\/abs\/1003.0564\">here<\/a>. They are constructed interactively using the mouse GUI (or manually through keyboard entry of the node \/ line tables) from this <a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/ToE_Demonstration.nb\">Mathematica notebook<\/a> or free CDF player <a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/ToE_Demonstration.cdf\">demonstration document<\/a> or interactive CDF player <a href=\"http:\/\/theoryofeverything.org\/MyToE\/?page_id=755\">web page<\/a>.<\/p>\n<p>All of these demonstrations have now been updated to include the new options on Dynkin diagram creation, including left (vs. right) affine topology recognition, black&#038;white vs. color nodes and edges, and for those with full Mathematica licenses the notebook allows for added Dynkin line types.<\/p>\n<p>The Lie group names are calculated based on the Dynkin topology. The geometric permutation names are calculated (to rank 8) based on the binary pattern of empty and filled nodes. The node and line colors can be used as indicators in Coxeter projections and\/or Hasse diagrams.<\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2005\" rel=\"attachment wp-att-2005\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank3CompactHyperbolicDynkins1-31bw.svg_.png\" alt=\"Rank3CompactHyperbolicDynkins1-31bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2005\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2006\" rel=\"attachment wp-att-2006\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank3NonCompactHyperbolicDynkins32-75bw.svg_.png\" alt=\"Rank3NonCompactHyperbolicDynkins32-75bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2006\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2016\" rel=\"attachment wp-att-2016\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank3NonCompactHyperbolicDynkins76-123bw.svg_.png\" alt=\"Rank3NonCompactHyperbolicDynkins76-123bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2016\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2007\" rel=\"attachment wp-att-2007\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank4HyperbolicDynkins124-176bw.svg_.png\" alt=\"Rank4HyperbolicDynkins124-176bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2007\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2015\" rel=\"attachment wp-att-2015\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank5HyperbolicDynkins177-198bw.svg_.png\" alt=\"Rank5HyperbolicDynkins177-198bw.svg\" width=\"500\" height=\"550\" class=\"alignnone size-full wp-image-2015\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2014\" rel=\"attachment wp-att-2014\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank6HyperbolicDynkins199-205bw.svg_.png\" alt=\"Rank6HyperbolicDynkins199-205bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2014\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2009\" rel=\"attachment wp-att-2009\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank6HyperbolicDynkins206-212bw.svg_.png\" alt=\"Rank6HyperbolicDynkins206-212bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2009\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2010\" rel=\"attachment wp-att-2010\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank6HyperbolicDynkins213-220bw.svg_.png\" alt=\"Rank6HyperbolicDynkins213-220bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2010\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2008\" rel=\"attachment wp-att-2008\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank7HyperbolicDynkins221-224bw.svg_.png\" alt=\"Rank7HyperbolicDynkins221-224bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2008\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2019\" rel=\"attachment wp-att-2019\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank8HyperbolicDynkins225-229bw_svg1.png\" alt=\"Rank8HyperbolicDynkins225-229bw_svg\" width=\"500\" class=\"alignnone size-full wp-image-2019\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2020\" rel=\"attachment wp-att-2020\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank9HyperbolicDynkins230-234bw_svg.png\" alt=\"Rank9HyperbolicDynkins230-234bw_svg\" width=\"500\" class=\"alignnone size-full wp-image-2020\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2011\" rel=\"attachment wp-att-2011\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/08\/Rank10HyperbolicDynkins235-238bw.svg_.png\" alt=\"Rank10HyperbolicDynkins235-238bw.svg\" width=\"500\" class=\"alignnone size-full wp-image-2011\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I am pleased to announce the availability of the comprehensive set of 238 Hyperbolic Dynkin diagrams ranks 3 to 10. These are enumerated here. They are constructed interactively using the mouse GUI (or manually through keyboard entry of the node \/ line tables) from this Mathematica notebook or free CDF player demonstration document or interactive &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2013\/08\/10\/hyperbolic-dynkin-diagrams\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Hyperbolic Dynkin Diagrams<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[18],"class_list":["post-1356","post","type-post","status-publish","format-standard","hentry","category-physics","tag-dynkin"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"I am pleased to announce the availability of the comprehensive set of 238 Hyperbolic Dynkin diagrams ranks 3 to 10. 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