The tensor structure on the representation category of the \(\mathcal {W}_p\) triplet algebra (Q2863649)
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scientific article; zbMATH DE number 6232238
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The tensor structure on the representation category of the \(\mathcal {W}_p\) triplet algebra |
scientific article; zbMATH DE number 6232238 |
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25 November 2013
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triplet vertex algebra
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fusion tensor products
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braided monoidal category
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0.91188353
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0.89806175
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0.89792144
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0.8977477
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0.89730525
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0.89447534
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0.8941165
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0.89064896
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0.89012206
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The tensor structure on the representation category of the \(\mathcal {W}_p\) triplet algebra (English)
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In this paper, the authors study the representation category of the triplet vertex algebra \(\mathcal{W}(p)\). The irreducible modules for \(\mathcal{W}(p)\) were classified in [\textit{D. Adamović} and \textit{A. Milas}, Adv. Math. 217, No. 6, 2664--2699 (2008; Zbl 1177.17017)]. In the paper under review, the authors use the methods for computing fusion products, developed by W. Nahm, M. Gaberdiel and H. Kausch, to calculate fusion products for \(\mathcal{W}(p)\)-modules. They present a result that the braided monoidal structure on the category of \(\mathcal{W}(p)\)-modules is rigid. They also prove explicit formulas for fusion products of all simple and all projective modules.
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