{"id":732,"date":"2020-08-27T11:56:28","date_gmt":"2020-08-27T09:56:28","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=732"},"modified":"2020-08-27T11:56:28","modified_gmt":"2020-08-27T09:56:28","slug":"on-zhus-algebra-and-c_2-algebra-for-symplectic-fermion-vertex-algebra-sfd","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/hr\/on-zhus-algebra-and-c_2-algebra-for-symplectic-fermion-vertex-algebra-sfd\/","title":{"rendered":"On Zhu’s algebra and\u00a0\"C_2\"\u2013algebra for symplectic fermion vertex algebra\u00a0\"SF(d)^+\""},"content":{"rendered":"

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Authors:<\/strong>\u00a0Dra\u017een\u00a0<\/span>Adamovi\u0107<\/span>,\u00a0<\/span>Ante\u00a0<\/span>\u010ceperi\u0107<\/span><\/span><\/p>\n

Journal of Algebra,\u00a0Volume 563,\u00a01 December 2020, Pages 376-403,\u00a0https:\/\/doi.org\/10.1016\/j.jalgebra.2020.07.019<\/p>\n

Abstract:<\/strong>\u00a0In this paper, we study the family of vertex operator algebras\u00a0\"SF(d)^+\", known as symplectic fermions. This family is of a particular interest because these VOAs are irrational and\u00a0\"C_2\"-cofinite. We determine Zhu’s algebra\u00a0\"A(SF(d)^+)\"\u00a0and show that the equality of dimensions of\u00a0\"A(SF(d)^+)\"\u00a0and the\u00a0\"C_2\"-algebra\u00a0\"\mathcal{P}(SF(d)^+)\"\u00a0holds for\u00a0d\u22652<\/span><\/span><\/span>\u00a0(the case of\u00a0d=1<\/span><\/span><\/span>\u00a0was treated by T. Abe in\u00a0[1]<\/a>). We use these results to prove a conjecture by Y. Arike and K. Nagatomo ([8]<\/a>) on the dimension of the space of one-point functions on\u00a0\"SF(d)^+\".<\/p>\n

Keywords:<\/strong>\u00a0Vertex algebra,\u00a0Zhu’s algebra,\u00a0Symplectic fermions<\/p>\n

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

Authors:\u00a0Dra\u017een\u00a0Adamovi\u0107,\u00a0Ante\u00a0\u010ceperi\u0107 Journal of Algebra,\u00a0Volume 563,\u00a01 December 2020, Pages 376-403,\u00a0https:\/\/doi.org\/10.1016\/j.jalgebra.2020.07.019 Abstract:\u00a0In this paper, we study the family of vertex operator algebras\u00a0, known as symplectic fermions. This family is of a particular interest because these VOAs are irrational and\u00a0-cofinite. We determine Zhu’s algebra\u00a0\u00a0and show that the equality of dimensions of\u00a0\u00a0and the\u00a0-algebra\u00a0\u00a0holds for\u00a0d\u22652\u00a0(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\/hr\/wp-json\/wp\/v2\/posts\/732"}],"collection":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/comments?post=732"}],"version-history":[{"count":1,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/732\/revisions"}],"predecessor-version":[{"id":733,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/732\/revisions\/733"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/media?parent=732"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/categories?post=732"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/tags?post=732"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}