{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1362262946112201088.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1142/s0219199708003083"}},{"identifier":{"@type":"URI","@value":"https://www.worldscientific.com/doi/pdf/10.1142/S0219199708003083"}}],"dc:title":[{"@value":"RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p>Let V be a simple vertex operator algebra satisfying the following conditions: (i) V<jats:sub>(n)</jats:sub>= 0 for n < 0, V<jats:sub>(0)</jats:sub>= ℂ1 and V′ is isomorphic to V as a V-module. (ii) Every ℕ-gradable weak V-module is completely reducible. (iii) V is C<jats:sub>2</jats:sub>-cofinite. (In the presence of Condition (i), Conditions (ii) and (iii) are equivalent to a single condition, namely, that every weak V-module is completely reducible.) Using the results obtained by the author in the formulation and proof of the general version of the Verlinde conjecture and in the proof of the Verlinde formula, we prove that the braided tensor category structure on the category of V-modules is rigid, balanced and nondegenerate. In particular, the category of V-modules has a natural structure of modular tensor category. We also prove that the tensor-categorical dimension of an irreducible V-module is the reciprocal of a suitable matrix element of the fusing isomorphism under a suitable basis.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1382262946112201088","@type":"Researcher","foaf:name":[{"@value":"YI-ZHI HUANG"}],"jpcoar:affiliationName":[{"@value":"Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"02191997"},{"@type":"EISSN","@value":"17936683"}],"prism:publicationName":[{"@value":"Communications in Contemporary Mathematics"}],"dc:publisher":[{"@value":"World Scientific Pub Co Pte Lt"}],"prism:publicationDate":"2008-11","prism:volume":"10","prism:number":"supp01","prism:startingPage":"871","prism:endingPage":"911"},"reviewed":"false","url":[{"@id":"https://www.worldscientific.com/doi/pdf/10.1142/S0219199708003083"}],"createdAt":"2008-11-19","modifiedAt":"2020-05-10","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1050574257159224192","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Urod algebras and Translation of W-algebras"}]},{"@id":"https://cir.nii.ac.jp/crid/1050584409373724416","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras"},{"@value":"Singularities of nilpotent Slodowy slices and collapsing levels of <i>W</i>-algebras"}]},{"@id":"https://cir.nii.ac.jp/crid/1050845760656616320","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"A remark on the C 2-cofiniteness condition on vertex algebras"},{"@value":"A remark on the <span class=\"mathjax-formula\" data-tex=\"$C_2$\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>C</mi> <mn>2</mn> </msub></math></span>-cofiniteness condition on vertex algebras"}]},{"@id":"https://cir.nii.ac.jp/crid/1360290617451068416","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Two-dimensional topological order and operator algebras"}]},{"@id":"https://cir.nii.ac.jp/crid/1360306905186929024","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Ordinary modules for vertex algebras of 𝔬𝔰𝔭\n                    <sub>1|2𝑛</sub>"}]},{"@id":"https://cir.nii.ac.jp/crid/1360567180532386944","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Introduction to W-Algebras and Their Representation Theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1360567183053883520","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS"}]},{"@id":"https://cir.nii.ac.jp/crid/1360572092366364672","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Duality of subregular\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.svg\">\n                      <mml:mi mathvariant=\"script\">W</mml:mi>\n                    </mml:math>\n                    -algebras and principal\n                    <mml:math 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