Manin pairs and moment maps revisited

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-06-04 DOI:10.1016/j.geomphys.2025.105556

Eckhard Meinrenken, Selim Tawfik

引用次数: 0

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 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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重新审视了许多对和矩图

具有D/ g值矩映射的准泊松g空间的概念是由Alekseev和Kosmann-Schwarzbach在1999年提出的。我们的主要结果是一个提升定理，建立了具有D/ g值矩映射的拟泊松g空间和具有D值矩映射的拟泊松G×G-spaces两类之间的双射对应关系。利用这一结果，我们给出了这些空间的融合和共轭的简单构造，以及来自模空间的新例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity