Anyonic quantum symmetries of finite spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909229048135680 |
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| author | Anshu Bhattacharjee, Suvrajit Rahaman, Atibur Roy, Sutanu |
| author_facet | Anshu Bhattacharjee, Suvrajit Rahaman, Atibur Roy, Sutanu |
| contents | We construct a braided analogue of the quantum permutation group and show that it is the universal braided compact quantum group acting on a finite space in the category of $\mathbb{Z}/N\mathbb{Z}$-$\textrm{C}^*$-algebras with a twisted monoidal structure. As an application, we prove the existence of braided quantum symmetries of finite, simple, undirected, circulant graphs, explicitly compute it for several examples, and obtain a generalization of a result of Banica in this direction. Finally, in an appendix, we briefly describe the irreducible representations of this braided analogue of the quantum permutation group and their fusion rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_08153 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Anyonic quantum symmetries of finite spaces Anshu Bhattacharjee, Suvrajit Rahaman, Atibur Roy, Sutanu Quantum Algebra Operator Algebras We construct a braided analogue of the quantum permutation group and show that it is the universal braided compact quantum group acting on a finite space in the category of $\mathbb{Z}/N\mathbb{Z}$-$\textrm{C}^*$-algebras with a twisted monoidal structure. As an application, we prove the existence of braided quantum symmetries of finite, simple, undirected, circulant graphs, explicitly compute it for several examples, and obtain a generalization of a result of Banica in this direction. Finally, in an appendix, we briefly describe the irreducible representations of this braided analogue of the quantum permutation group and their fusion rules. |
| title | Anyonic quantum symmetries of finite spaces |
| topic | Quantum Algebra Operator Algebras |
| url | https://arxiv.org/abs/2207.08153 |