Courant morphisms and moment maps
Symplectic Geometry
2008-07-18 v3 Differential Geometry
Abstract
We study Hamiltonian spaces associated with pairs (E,A), where E is a Courant algebroid and A\subset 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.
Cite
@article{arxiv.0801.1663,
title = {Courant morphisms and moment maps},
author = {Henrique Bursztyn and David Iglesias Ponte and Pavol Severa},
journal= {arXiv preprint arXiv:0801.1663},
year = {2008}
}
Comments
18 pages. v2: Minor corrections, one example (Example 2.11) added. v3: Remark 2.5 fixed. To appear in Math. Research Letters