Lie group valued moment maps

Anton Alekseev, Anton Malkin, Eckhard Meinrenken

Type: Article

Publication Date: 1998-01-01

Citations: 433

DOI: https://doi.org/10.4310/jdg/1214460860

Abstract

We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra.The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg symplectic cross-section theorem and of convexity properties of the moment map.As an application we obtain moduli spaces of flat connections on an oriented compact 2-manifold with boundary as quasi-Hamiltonian quotients of the space G X • • • X G .

Locations

Journal of Differential Geometry - View - PDF
arXiv (Cornell University) - PDF

Similar Works

Action	Title	Year	Authors
+	Lie Group Valued Moment Maps	1997	Anton Alekseev Anton Malkin Eckhard Meinrenken
+	On Generalized Moment Maps for Symplectic Compact Group Actions	2003	Pierre Sleewaegen
+	A real convexity theorem for quasi-hamiltonian actions	2007	Florent Schaffhauser
+	Convexity of Hamiltonian manifolds	2001	Friedrich Knop
+ PDF Chat	Un théorème de convexité réel pour les applications moment à valeurs dans un groupe de Lie	2007	Florent Schaffhauser
+ PDF Chat	Manin Pairs and Moment Maps	2000	Anton Alekseev Yvette Kosmann–Schwarzbach
+	On the moment map on symplectic manifolds	2009	Leonardo Biliotti
+	Convexity of Hamiltonian manifolds	2001	Friedrich Knop
+	Manin pairs and moment maps	1999	Anton Alekseev Yvette Kosmann–Schwarzbach
+	On the moment map on symplectic manifolds	2006	Leonardo Biliotti
+	Symplectic group actions	2017	Dusa McDuff Dietmar Salamon
+ PDF Chat	Connectivity properties of moment maps on based loop groups	2006	Megumi Harada Tara S. Holm Lisa C. Jeffrey Augustin-Liviu Mare
+	Courant morphisms and moment maps	2008	Henrique Bursztyn David Iglesias Ponte Pavol Ševera
+ PDF Chat	Geometric quantization for proper moment maps: the Vergne conjecture	2012	Xiaonan Ma Weiping Zhang
+ PDF Chat	Convexity properties of the moment map for certain non-compact manifolds	1994	Elisa Prato
+ PDF Chat	Courant morphisms and moment maps	2009	Henrique Bursztyn David Iglesias Ponte Pavol Ševera
+ PDF Chat	The convexity package for Hamiltonian actions on conformal symplectic manifolds	2020	Youming Chen Reyer Sjamaar Xiangdong Yang
+	The convexity package for Hamiltonian actions on conformal symplectic manifolds	2019	Youming Chen Reyer Sjamaar Xiangdong Yang
+	The Moduli Space of Flat Connections over Higher Dimensional Manifolds	2018	Casey Blacker
+	Convexity Properties of the Moment Mapping Re-examined	1994	Reyer Sjamaar

Works That Cite This (423)

Action	Title	Year	Authors
+ PDF Chat	Symplectic Geometry and Isomonodromic Deformations	1999	Philip Boalch
+	Dirac structures and Dixmier-Douady bundles	2009	Anton Alekseev Eckhard Meinrenken
+ PDF Chat	An index theorem for loop spaces	2024	Doman Takata
+ PDF Chat	Verlinde Formulas for Nonsimply Connected Groups	2018	Eckhard Meinrenken
+ PDF Chat	Un théorème de convexité réel pour les applications moment à valeurs dans un groupe de Lie	2007	Florent Schaffhauser
+	Stokes phenomenon, Gelfand–Zeitlin systems and relative Ginzburg–Weinstein linearization	2018	Xiaomeng Xu
+	A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>K</mml:mi></mml:math>-homological approach to the quantization commutes with reduction problem	2016	Yanli Song
+	Noncommutative Networks on a Cylinder	2020	Nicholas Ovenhouse Michael Shapiro Semeon Arthamonov
+ PDF Chat	Twisted moduli spaces and Duistermaat–Heckman measures	2020	Ahmed J. Zerouali
+ PDF Chat	Flat Connections and the Commutator Map for SU(2)	2020	Nan-Kuo Ho Lisa C. Jeffrey Paul Selick Eugene Z. Xia

Works Cited by This (27)

Action	Title	Year	Authors
+	The Geometry of Four-Manifolds	1990	Simon Donaldson P. B. Kronheimer
+	Fusion of Hamiltonian loop group manifolds and cobordism	1997	Eckhard Meinrenken Chris Woodward
+	Poisson Lie groups, dressing transformations, and Bruhat decompositions	1990	Jiang-Hua Lu Alan Weinstein
+	Momentum Mappings And Reduction of Poisson Actions	1991	Jiang-Hua Lu
+ PDF Chat	A convexity theorem for Poisson actions of compact Lie groups	1996	H. Flaschka Tudor S. Raţiu
+	Group systems, groupoids, and moduli spaces of parabolic bundles	1997	K. Guruprasad Johannes Huebschmann Lisa C. Jeffrey Alan Weinstein
+ PDF Chat	Symplectic structure of the moduli space of flat connection on a Riemann surface	1995	Anton Alekseev Anton Malkin
+ PDF Chat	An algebraic proof for the symplectic structure of moduli space	1992	Yael Karshon
+ PDF Chat	Group cohomology construction of the cohomology of moduli spaces of flat connections on 2-manifolds	1995	Lisa C. Jeffrey
+	Boundary value problems for Yang—Mills fields	1992	Simon Donaldson