Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866909980273147904 |
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| author | Ferrer, Giovanni Palomares, Roberto Hernandez |
| author_facet | Ferrer, Giovanni Palomares, Roberto Hernandez |
| contents | Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker. We introduce unitary modules for these generalized TLJ 2-categories as strong *-pseudofunctors into the *-2-category of row-finite separable bigraded Hilbert spaces. We classify these modules up to *-equivalence in terms of weighted bi-directed fair and balanced graphs in the spirit of Yamagami's classification of fiber functors on TLJ categories and DeCommer and Yamashita's classification of unitary modules for Rep(SUq(2)). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1905_00471 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories Ferrer, Giovanni Palomares, Roberto Hernandez Operator Algebras Quantum Algebra 18D05 (Primary) 18D20, 20G42 (Secondary) Generalized Temperley-Lieb-Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker. We introduce unitary modules for these generalized TLJ 2-categories as strong *-pseudofunctors into the *-2-category of row-finite separable bigraded Hilbert spaces. We classify these modules up to *-equivalence in terms of weighted bi-directed fair and balanced graphs in the spirit of Yamagami's classification of fiber functors on TLJ categories and DeCommer and Yamashita's classification of unitary modules for Rep(SUq(2)). |
| title | Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories |
| topic | Operator Algebras Quantum Algebra 18D05 (Primary) 18D20, 20G42 (Secondary) |
| url | https://arxiv.org/abs/1905.00471 |