Central extensions for loop groups of area-preserving diffeomorphisms and their fuzzy sphere limits
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912950744252416 |
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| author | Janssens, Bas Wang, Zhenghan |
| author_facet | Janssens, Bas Wang, Zhenghan |
| contents | We classify central extensions for the loop group LSDiff(S^2) of area-preserving diffeomorphisms of the 2-sphere, and of related twisted loop groups. We then show that the corresponding Lie algebra cocycles are `fuzzy sphere limits' of Kac-Moody cocycles for (twisted) loop algebras Lsu(k+1) for the limit of large k, provided that the cocycles are rescaled by 6/k^3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06876 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Central extensions for loop groups of area-preserving diffeomorphisms and their fuzzy sphere limits Janssens, Bas Wang, Zhenghan Mathematical Physics Differential Geometry 17B65, 22E65, 17B67, 53D50 We classify central extensions for the loop group LSDiff(S^2) of area-preserving diffeomorphisms of the 2-sphere, and of related twisted loop groups. We then show that the corresponding Lie algebra cocycles are `fuzzy sphere limits' of Kac-Moody cocycles for (twisted) loop algebras Lsu(k+1) for the limit of large k, provided that the cocycles are rescaled by 6/k^3. |
| title | Central extensions for loop groups of area-preserving diffeomorphisms and their fuzzy sphere limits |
| topic | Mathematical Physics Differential Geometry 17B65, 22E65, 17B67, 53D50 |
| url | https://arxiv.org/abs/2603.06876 |