{"id":112,"date":"2017-02-21T20:11:46","date_gmt":"2017-02-21T20:11:46","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/pgrseminars\/?p=112"},"modified":"2017-02-21T20:12:58","modified_gmt":"2017-02-21T20:12:58","slug":"17th-february-joe","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2017\/02\/21\/17th-february-joe\/","title":{"rendered":"17th February &#8211; Joe: Cluster&#8217;s first stand"},"content":{"rendered":"<p>Special types of cluster algebra arise from quiver mutation. In general these have infinitely many generators. Fomin and Zelevinsky provided a criterion for the finite case in terms of simply laced Dynkin diagrams, also constructing a bijection from the &#8220;almost positive&#8221; roots of the associated root system to the set of cluster variables. \u00a0\u00a0If one looks at representations \u00a0of (some orientation of)\u00a0the ADE diagrams, Gabriel&#8217;s theorem gives a bijection from the isomorphism\u00a0classes of irreducible representations to the positive roots of the root system.\u00a0 This\u00a0can be combined with Fomin and Zelevinsky&#8217;s bijection. I&#8217;ll explain some of the basics of cluster algebras and demonstrate these results with a simple example.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Special types of cluster algebra arise from quiver mutation. In general these have infinitely many generators. Fomin and Zelevinsky provided a criterion for the finite &hellip; <a href=\"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2017\/02\/21\/17th-february-joe\/\">Read&nbsp;more<\/a><\/p>\n","protected":false},"author":46264,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/112"}],"collection":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/users\/46264"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/comments?post=112"}],"version-history":[{"count":2,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/112\/revisions"}],"predecessor-version":[{"id":114,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/112\/revisions\/114"}],"wp:attachment":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/media?parent=112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/categories?post=112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/tags?post=112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}