{"id":576,"date":"2018-02-20T11:44:47","date_gmt":"2018-02-20T09:44:47","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=576"},"modified":"2018-02-20T11:46:14","modified_gmt":"2018-02-20T09:46:14","slug":"conformal-embeddings-of-affine-vertex-algebras-in-minimal-w-algebras-i-structural-results","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/conformal-embeddings-of-affine-vertex-algebras-in-minimal-w-algebras-i-structural-results\/","title":{"rendered":"Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results"},"content":{"rendered":"

<\/span><\/p>\n

Authors:\u00a0<\/span>Dra\u017een Adamovi\u0107, Victor G. Kac, Pierluigi M\u00f6seneder Frajria, Paolo Papi, Ozren Per\u0161e<\/p>\n

Journal of Algebra,
\nVolume 500,
\n2018,
\nPages 117-152,
\nISSN 0021-8693,
\nhttps:\/\/doi.org\/10.1016\/j.jalgebra.2016.12.005<\/a>
\n(http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021869316304604<\/a>)<\/p>\n

Abstract: We find all values of \"k \in \mathbb{C}\", for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra \"W_k(\mathfrak{g},\theta)\" is conformal, where \"\mathfrak{g}\",is a basic simple Lie superalgebra and\u00a0\"-\theta\" its minimal root. In particular, it turns out that if \"W_k(\mathfrak{g},\theta)\" does not collapse to its affine part, then the possible values of these k are either \"−\frac{2}{3}h^\vee\" or \u00a0\"−\frac{h^\vee-1}{2}\", where\u00a0\"h^\vee\" is the dual Coxeter number of \"\mathfrak{g}\" for the normalization \"(\theta,\theta)=2\". As an application of our results, we present a realization of simple affine vertex algebra \"V_{-\frac{n-1}{2}}(sl(n+1))\" inside the tensor product of the vertex algebra \"W_{-\frac{n-1}{2}}(sl(2|n),\theta)\" (also called the Bershadsky\u2013Knizhnik algebra) with a lattice vertex algebra.<\/p>\n

MSC: primary 17B69,\u00a0secondary 17B20, 17B65<\/div>\n

Keywords: Vertex algebra; Virasoro (=conformal) vector; Conformal embedding; Conformal level; Collapsing level<\/p>\n

<\/dl>\n

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

Authors:\u00a0Dra\u017een Adamovi\u0107, Victor G. Kac, Pierluigi M\u00f6seneder Frajria, Paolo Papi, Ozren Per\u0161e Journal of Algebra, Volume 500, 2018, Pages 117-152, ISSN 0021-8693, https:\/\/doi.org\/10.1016\/j.jalgebra.2016.12.005 (http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021869316304604) Abstract: We find all values of , for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra is conformal, where ,is […]<\/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\/576"}],"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=576"}],"version-history":[{"count":13,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/576\/revisions"}],"predecessor-version":[{"id":590,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/576\/revisions\/590"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media?parent=576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/categories?post=576"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/tags?post=576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}