Invertible projective 2-representations from invertible 2d TQFTs with defects
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909798526615552 |
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| author | Fiorenza, Domenico Vuppulury, Chetan |
| author_facet | Fiorenza, Domenico Vuppulury, Chetan |
| contents | We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the 1-categorical setting, this result becomes interesting for 2-representations: as an application, only relying only on invertibility of Clifford algebras and Fock bimodules in the Morita 2-category of super vector spaces we recover Ludewig--Roos' result that the Clifford/Fock construction is a projective 2-representation of the category of Lagrangian correspondences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invertible projective 2-representations from invertible 2d TQFTs with defects Fiorenza, Domenico Vuppulury, Chetan Category Theory Mathematical Physics Quantum Algebra Representation Theory 57R56 We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the 1-categorical setting, this result becomes interesting for 2-representations: as an application, only relying only on invertibility of Clifford algebras and Fock bimodules in the Morita 2-category of super vector spaces we recover Ludewig--Roos' result that the Clifford/Fock construction is a projective 2-representation of the category of Lagrangian correspondences. |
| title | Invertible projective 2-representations from invertible 2d TQFTs with defects |
| topic | Category Theory Mathematical Physics Quantum Algebra Representation Theory 57R56 |
| url | https://arxiv.org/abs/2509.16626 |