{"id":1448,"date":"2010-05-08T13:51:59","date_gmt":"2010-05-08T06:51:59","guid":{"rendered":"http:\/\/www.math.itb.ac.id\/?p=1448"},"modified":"2010-05-08T13:51:59","modified_gmt":"2010-05-08T06:51:59","slug":"1-feb-7-mei-2010-a-course-on-leavitt-path-algebras","status":"publish","type":"post","link":"https:\/\/multisite.itb.ac.id\/math\/2010\/05\/08\/1-feb-7-mei-2010-a-course-on-leavitt-path-algebras\/","title":{"rendered":"1 Feb~7 Mei 2010: A Course on Leavitt path algebras\u00a0"},"content":{"rendered":"<p style=\"text-align: center\"><strong><span class=\"TextRun SCXW168292114\" lang=\"EN-US\" xml:lang=\"EN-US\"><span class=\"NormalTextRun SCXW168292114\">MA 6211 Advanced Topic in Algebra<\/span><\/span><\/strong><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"54\" data-aria-posinset=\"1\" data-aria-level=\"1\">Prof.Gonzalo\u00a0Aranda Pino (Universitas\u00a0Malaga,\u00a0Spanyol)\u202f(Feb 1 \u2013 Feb 26, 2010)<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<\/ul>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"54\" data-aria-posinset=\"1\" data-aria-level=\"1\">Dr.\u00a0Intan\u00a0Muchtadi\u00a0(March 1 -\u202f May 7, 2010)<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<\/ul>\n<p>every Tuesday 11.00-12.40 and every\u202fThursday 09.00-10.40<span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>This course is, in part, an adaptation of Enrique Pardo and Mercedes\u00a0Siles\u00a0Molina\u2019s notes of the course \u201cAlgebras and Graphs\u201d that was held at the University of M\u00e1laga during Winter 2009 (and will be held again in Winter 2010) as part of the Interdepartmental Master\u2019s Degree in Mathematics.<span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>Leavitt path algebras are a specific type of path K-algebras associated to a graph E, modulo some relations, and are denoted by L(E). They can be considered, on the one hand, as natural generalizations of Leavitt algebras L(1,m) of type (1,m), introduced and investigated by Leavitt in order to give examples of algebras not satisfying the IBN property (i.e., of algebras that can have bases of different cardinals). On the other hand, they are the algebraic version of\u00a0Cuntz-Krieger graph C<span data-fontsize=\"10\">*<\/span>-algebras, a class of algebras intensively investigated by analysts for more than two decades.<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>Besides the classical Leavitt algebras L(1,m), many other well-known algebras can be realized as the Leavitt path algebra of a graph, some of those include matrix algebras of finite or infinite size, Laurent polynomials, Toeplitz algebras, etc. Further, constructions such as direct sums, direct limits and combinations of all of the above can be also obtained.<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>In this sense Leavitt path algebras provide a pictorial, and hence very convenient and useful, representation of abstract rings and algebras and thus the focus of this course is try to give an introduction to the subject by characterizing some of the most basic properties of L(E) in terms of graph theoretic properties of E such as finite-dimensionality, simplicity and purely infinite simplicity.<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><strong><em>REFERENCES:\u00a0<\/em><\/strong><\/p>\n<p>[1] G. Abrams, G. Aranda Pino, \u201cThe Leavitt path algebra of a graph\u201d,\u202f<i>J. Algebra<\/i>\u00a0293 (2005), 319-334.<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>[2] G. Abrams, G. Aranda Pino, M.\u00a0Siles\u00a0Molina, \u201cFinite-dimensional Leavitt path algebras\u201d,\u202f<i>J. Pure Appl. Algebra<\/i>\u00a0209 (3) (2007), 753&#8211;762.<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>[3] P. Ara, M.A. Moreno, E. Pardo, \u201cNonstable K-theory for graph algebras\u201d,\u202f<i>Algebras &amp; Representation Theory<\/i>, 10 (2007), 157-178.<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>[4] I. Raeburn, \u201cGraph algebras\u201d.\u202f<i>CBMS Regional Conference Series in Mathematics<\/i>, 103, American Mathematical Society, Providence, 2005. ISBN 0-8218-3660-9.<span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>MA 6211 Advanced Topic in Algebra Prof.Gonzalo\u00a0Aranda Pino (Universitas\u00a0Malaga,\u00a0Spanyol)\u202f(Feb 1 \u2013 Feb 26, 2010)\u00a0 Dr.\u00a0Intan\u00a0Muchtadi\u00a0(March 1 -\u202f May 7, 2010)\u00a0 every Tuesday 11.00-12.40 and every\u202fThursday 09.00-10.40\u00a0 \u00a0 This course is, in part, an adaptation of Enrique Pardo and Mercedes\u00a0Siles\u00a0Molina\u2019s notes of the course \u201cAlgebras and Graphs\u201d that was held at the University of M\u00e1laga during [&hellip;]<\/p>\n","protected":false},"author":1479,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,29],"tags":[],"class_list":["post-1448","post","type-post","status-publish","format-standard","hentry","category-algebra","category-events"],"_links":{"self":[{"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/posts\/1448","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/users\/1479"}],"replies":[{"embeddable":true,"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/comments?post=1448"}],"version-history":[{"count":0,"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/posts\/1448\/revisions"}],"wp:attachment":[{"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/media?parent=1448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/categories?post=1448"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/multisite.itb.ac.id\/math\/wp-json\/wp\/v2\/tags?post=1448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}