Affine modules and the Drinfeld Center
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2010
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| _version_ | 1866908738565177344 |
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| author | Das, Paramita Ghosh, Shamindra Kumar Gupta, Ved Prakash |
| author_facet | Das, Paramita Ghosh, Shamindra Kumar Gupta, Ved Prakash |
| contents | Given a finite index subfactor, we show that the {\em affine morphisms at zero level} in the affine category over the planar algebra associated to the subfactor is isomorphic to the fusion algebra of the subfactor as a *-algebra. This identification paves the way to analyze the structure of affine $P$-modules with weight zero for any subfactor planar algebra $P$ (possibly having infinite depth). Further, for irreducible depth two subfactor planar algebras, we establish an additive equivalence between the category of affine $P$-modules and the center of the category of $N$-$N$-bimodules generated by $L^2(M)$; this partially verifies a conjecture of Jones and Walker. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1010_0460 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Affine modules and the Drinfeld Center Das, Paramita Ghosh, Shamindra Kumar Gupta, Ved Prakash Quantum Algebra Operator Algebras 46L37 Given a finite index subfactor, we show that the {\em affine morphisms at zero level} in the affine category over the planar algebra associated to the subfactor is isomorphic to the fusion algebra of the subfactor as a *-algebra. This identification paves the way to analyze the structure of affine $P$-modules with weight zero for any subfactor planar algebra $P$ (possibly having infinite depth). Further, for irreducible depth two subfactor planar algebras, we establish an additive equivalence between the category of affine $P$-modules and the center of the category of $N$-$N$-bimodules generated by $L^2(M)$; this partially verifies a conjecture of Jones and Walker. |
| title | Affine modules and the Drinfeld Center |
| topic | Quantum Algebra Operator Algebras 46L37 |
| url | https://arxiv.org/abs/1010.0460 |