Drinfeld center of planar algebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2012
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| _version_ | 1866909978194870272 |
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| author | Das, Paramita Ghosh, Shamindra Kumar Gupta, Ved Prakash |
| author_facet | Das, Paramita Ghosh, Shamindra Kumar Gupta, Ved Prakash |
| contents | We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N \subset M$ is a subfactor realization of $P$, then the Drinfeld center of the $N$-$N$-bimodule category generated by $_N L^2 (M)_M$, is equivalent to the category of Hilbert affine representations of $P$ satisfying certain finiteness criterion. As a consequence, we prove Kevin Walker's conjecture for planar algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1203_3958 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Drinfeld center of planar algebra Das, Paramita Ghosh, Shamindra Kumar Gupta, Ved Prakash Quantum Algebra Category Theory Operator Algebras 46L37 We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N \subset M$ is a subfactor realization of $P$, then the Drinfeld center of the $N$-$N$-bimodule category generated by $_N L^2 (M)_M$, is equivalent to the category of Hilbert affine representations of $P$ satisfying certain finiteness criterion. As a consequence, we prove Kevin Walker's conjecture for planar algebras. |
| title | Drinfeld center of planar algebra |
| topic | Quantum Algebra Category Theory Operator Algebras 46L37 |
| url | https://arxiv.org/abs/1203.3958 |