Unitary anchored planar algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916218994163712 |
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| author | Henriques, André Penneys, David Tener, James |
| author_facet | Henriques, André Penneys, David Tener, James |
| contents | In our previous article [arXiv:1607.06041], we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the notion of unitarity for both module tensor categories and anchored planar algebras, and establishes the unitary analog of the above equivalence. Our constructions use Baez's 2-Hilbert spaces (i.e., semisimple $C^*$-categories equipped with unitary traces), the unitary Yoneda embedding, and the notion of unitary adjunction for dagger functors between 2-Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11114 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unitary anchored planar algebras Henriques, André Penneys, David Tener, James Quantum Algebra Category Theory 18M05, 18M30, 18M40, 18M65 In our previous article [arXiv:1607.06041], we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the notion of unitarity for both module tensor categories and anchored planar algebras, and establishes the unitary analog of the above equivalence. Our constructions use Baez's 2-Hilbert spaces (i.e., semisimple $C^*$-categories equipped with unitary traces), the unitary Yoneda embedding, and the notion of unitary adjunction for dagger functors between 2-Hilbert spaces. |
| title | Unitary anchored planar algebras |
| topic | Quantum Algebra Category Theory 18M05, 18M30, 18M40, 18M65 |
| url | https://arxiv.org/abs/2301.11114 |