Density and unitarity of the Burau representation from a non-semisimple TQFT
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909761426948096 |
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| author | Geer, Nathan Lauda, Aaron D. Patureau-Mirand, Bertrand Sussan, Joshua |
| author_facet | Geer, Nathan Lauda, Aaron D. Patureau-Mirand, Bertrand Sussan, Joshua |
| contents | We study the density of the Burau representation from the perspective of a non-semisimple TQFT at a fourth root of unity. This gives a TQFT construction of Squier's Hermitian form on the Burau representation with possibly mixed signature. We prove that the image of the braid group in the space of possibly indefinite unitary representations is dense. We also argue for the potential applications of non-semisimple TQFTs toward topological quantum computation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_13242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density and unitarity of the Burau representation from a non-semisimple TQFT Geer, Nathan Lauda, Aaron D. Patureau-Mirand, Bertrand Sussan, Joshua Geometric Topology Quantum Algebra Representation Theory Quantum Physics 81R50, 57R56, 22D10, 46N50 We study the density of the Burau representation from the perspective of a non-semisimple TQFT at a fourth root of unity. This gives a TQFT construction of Squier's Hermitian form on the Burau representation with possibly mixed signature. We prove that the image of the braid group in the space of possibly indefinite unitary representations is dense. We also argue for the potential applications of non-semisimple TQFTs toward topological quantum computation. |
| title | Density and unitarity of the Burau representation from a non-semisimple TQFT |
| topic | Geometric Topology Quantum Algebra Representation Theory Quantum Physics 81R50, 57R56, 22D10, 46N50 |
| url | https://arxiv.org/abs/2402.13242 |