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arXiv · 2404.17518

Manin pairs and moment maps revisited

Eckhard Meinrenken·Selim Tawfik
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Abstract

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.

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Eckhard Meinrenken, Selim Tawfik. 2025-05-03. Manin pairs and moment maps revisited. https://arxiv.org/abs/2404.17518

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