Manin pairs and moment maps revisited
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915271715848192 |
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| author | Meinrenken, Eckhard Tawfik, Selim |
| author_facet | Meinrenken, Eckhard Tawfik, Selim |
| contents | The notion of quasi-Poisson $G$-spaces with $D/G$-valued moment maps was introduced by Alekseev and Kosmann-Schwarzbach in 1999. Our main result is a \emph{Lifting Theorem}, establishing a bijective correspondence between the categories of quasi-Poisson $G$-spaces with $D/G$-valued moment maps and of quasi-Poisson $G\times G$-spaces with $D$-valued moment maps. Using this result, we give simple constructions of fusion and conjugation for these spaces, and new examples coming from moduli spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Manin pairs and moment maps revisited Meinrenken, Eckhard Tawfik, Selim Differential Geometry 53D17 The notion of quasi-Poisson $G$-spaces with $D/G$-valued moment maps was introduced by Alekseev and Kosmann-Schwarzbach in 1999. Our main result is a \emph{Lifting Theorem}, establishing a bijective correspondence between the categories of quasi-Poisson $G$-spaces with $D/G$-valued moment maps and of quasi-Poisson $G\times G$-spaces with $D$-valued moment maps. Using this result, we give simple constructions of fusion and conjugation for these spaces, and new examples coming from moduli spaces. |
| title | Manin pairs and moment maps revisited |
| topic | Differential Geometry 53D17 |
| url | https://arxiv.org/abs/2404.17518 |