Courant morphisms and moment maps

2008/01/10 by Bursztyn, Henrique, Ponte, David Iglesias, Severa, Pavol · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0801.1663

Abstract

We study Hamiltonian spaces associated with pairs (E,A), where E is a Courant algebroid and A⊂ E is a Dirac structure. These spaces are defined in terms of morphisms of Courant algebroids with suitable compatibility conditions. Several of their properties are discussed, including a reduction procedure. This set-up encompasses familiar moment map theories, such as group-valued moment maps, and it provides an intrinsic approach from which different geometrical descriptions of moment maps can be naturally derived. As an application, we discuss the relationship between quasi-Poisson and presymplectic groupoids.

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