{"id":595,"date":"2024-04-29T01:26:16","date_gmt":"2024-04-29T01:26:16","guid":{"rendered":"https:\/\/src.cikeys.com\/2024\/?page_id=595"},"modified":"2024-04-29T01:26:16","modified_gmt":"2024-04-29T01:26:16","slug":"octonions-as-tensors-and-their-multiplication","status":"publish","type":"page","link":"https:\/\/src.cikeys.com\/2024\/conference-schedule\/poster-presentations\/poster-presentations-session-3\/octonions-as-tensors-and-their-multiplication\/","title":{"rendered":"Octonions as Tensors and their Multiplication"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Jackson Seligman, &amp; Dr. Ivona Grzegorczyk<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">In this presentation, I am investigating Octonions (O) as rank three tensors, their multiplication, and their various constructions Octonions are an Algebra that have the following properties: The are non-commutative (ab \u0338 = ba) nor are they anti-commutative (ab \u0338 = -ba). They also are non-associative as (a(bc)\u0338 =(ab)c). They do however abide by the basis square multiplication of: e2_1 = e2_2 = e2_3 = e2_4 = e2_5 = e2_6 = e2_7 = \u22121 = \u2212(e0)2 where e0 is the real basis and e1, e2, e3, e4, e5, e6, e7 are the imaginary basis, also known as the 7 vector portion of the octonion.<br><br>Octonions are an extension of quaternions with additional imaginary basis e_4 with the associated multiplication giving 8 basis. They pose an important role at the current edge of particle physics research being the mathematical system proposed to describe supersymmetry.<br><br>A common issue with octonions is that they are not associative. They are commonly attempted to be transformed into matrices which in themselves are associative. This is a contradiction but is considered necessary by many physicists. This will also be investigated as it is currently under great debate.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/src.cikeys.com\/2024\/conference-schedule\/poster-presentations\/\"><strong>Poster Presentation<\/strong><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/src.cikeys.com\/2024\/conference-schedule\/poster-presentations\/poster-presentations-session-3\/\">Session 3<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2:45pm&nbsp;<strong>\u2013<\/strong>&nbsp;4:00pm<br>Grand Salon<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mathematics<\/strong><\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Jackson Seligman, &amp; Dr. Ivona Grzegorczyk In this presentation, I am investigating Octonions (O) as rank three tensors, their multiplication, and their various constructions Octonions are an Algebra that have the following properties: The are non-commutative (ab \u0338 = ba) nor are they anti-commutative (ab \u0338 = -ba). They also are non-associative as (a(bc)\u0338 =(ab)c). [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":48,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[5,8],"tags":[31],"class_list":["post-595","page","type-page","status-publish","hentry","category-poster-presentations","category-session-3","tag-mathematics","post"],"_links":{"self":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/595","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/comments?post=595"}],"version-history":[{"count":1,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/595\/revisions"}],"predecessor-version":[{"id":643,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/595\/revisions\/643"}],"up":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/48"}],"wp:attachment":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/media?parent=595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/categories?post=595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/tags?post=595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}