On the coadjoint Virasoro action
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910288044883968 |
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| author | Alekseev, Anton Meinrenken, Eckhard |
| author_facet | Alekseev, Anton Meinrenken, Eckhard |
| contents | The set of coadjoint orbits of the Virasoro algebra at level 1 is in bijection with the set of conjugacy classes in a certain open subset $\widetilde{\rm SL}(2,\mathbb{R})_+$ of the universal cover of ${\rm SL}(2,\mathbb{R})$. We strengthen this bijection to a Morita equivalence of quasi-symplectic groupoids, integrating the Poisson structure on $\mathfrak{vir}^*_\mathsf{1}(S^1)$ and the Cartan-Dirac structure on $\widetilde{\rm SL}(2,\mathbb{R})_+$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06216 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the coadjoint Virasoro action Alekseev, Anton Meinrenken, Eckhard Differential Geometry Mathematical Physics The set of coadjoint orbits of the Virasoro algebra at level 1 is in bijection with the set of conjugacy classes in a certain open subset $\widetilde{\rm SL}(2,\mathbb{R})_+$ of the universal cover of ${\rm SL}(2,\mathbb{R})$. We strengthen this bijection to a Morita equivalence of quasi-symplectic groupoids, integrating the Poisson structure on $\mathfrak{vir}^*_\mathsf{1}(S^1)$ and the Cartan-Dirac structure on $\widetilde{\rm SL}(2,\mathbb{R})_+$, respectively. |
| title | On the coadjoint Virasoro action |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2211.06216 |