{"id":734,"date":"2020-08-27T12:01:42","date_gmt":"2020-08-27T10:01:42","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=734"},"modified":"2020-08-27T12:01:42","modified_gmt":"2020-08-27T10:01:42","slug":"classification-of-irreducible-modules-for-bershadsky-polyakov-algebra-at-certain-levels","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/classification-of-irreducible-modules-for-bershadsky-polyakov-algebra-at-certain-levels\/","title":{"rendered":"Classification of irreducible modules for Bershadsky\u2013Polyakov algebra at certain levels"},"content":{"rendered":"

<\/p>\n

Authors:<\/strong> Dra\u017een Adamovi\u0107,\u00a0Ana Kontrec<\/div>\n
Journal of Algebra and its applications (2020),\u00a0https:\/\/doi.org\/10.1142\/S0219498821501024<\/a><\/div>\n
<\/div>\n
Abstract:\u00a0<\/strong><\/strong>We study the representation theory of the Bershadsky-Polyakov algebra \"\mathcal W_k = \mathcal{W}_k(sl_3,f_{\theta})\". In particular, Zhu algebra of \"\mathcal W_k\" is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category \"\mathcal{O}\" for the Bershadsky-Polyakov algebra \"\mathcal W_k\" for \"k=-5/3, -9/4, -1,0\". In the case \"k=0\" we show that the Zhu algebra \"A(\mathcal W_k)\" has \"2\"–dimensional indecomposable modules.<\/p>\n
<\/div>\n
Keywords:\u00a0<\/strong>Vertex algebra,\u00a0W<\/span><\/span><\/span>W<\/span><\/span><\/span>-algebras,\u00a0Bershadsky\u2013Polyakov algebra,\u00a0Zhu\u2019s algebra<\/div>\n<\/div>\n

<\/p>","protected":false},"excerpt":{"rendered":"

Authors: Dra\u017een Adamovi\u0107,\u00a0Ana Kontrec Journal of Algebra and its applications (2020),\u00a0https:\/\/doi.org\/10.1142\/S0219498821501024 Abstract:\u00a0We study the representation theory of the Bershadsky-Polyakov algebra . In particular, Zhu algebra of is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category for the […]<\/a><\/p>\n<\/div>","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[18,14],"tags":[],"_links":{"self":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/734"}],"collection":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/comments?post=734"}],"version-history":[{"count":1,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/734\/revisions"}],"predecessor-version":[{"id":735,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/734\/revisions\/735"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media?parent=734"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/categories?post=734"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/tags?post=734"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}