Manin pairs and moment maps revisited
Eckhard Meinrenken, Selim Tawfik

TL;DR
This paper revisits the theory of quasi-Poisson spaces with moment maps, establishing a bijective correspondence between different categories and providing new constructions and examples, including from moduli spaces.
Contribution
It introduces a Lifting Theorem linking categories of quasi-Poisson spaces with different moment map values, enabling new constructions and examples.
Findings
Established a bijective correspondence between categories of quasi-Poisson spaces.
Provided new constructions of fusion and conjugation for these spaces.
Presented new examples from moduli spaces.
Abstract
The notion of quasi-Poisson -spaces with -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 -spaces with -valued moment maps and of quasi-Poisson -spaces with -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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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic structures and combinatorial models
