Courant morphisms and moment maps

Details Courant morphisms and moment maps Courant morphisms and moment maps

2008-01-10

arxiv.org/abs/0801.1663v3

Mathematics

Symplectic Geometry

18 pages. v2: Minor corrections, one example (Example 2.11) added. v3: Remark 2.5 fixed. To appear in Math. Research Letters

Scientific paper

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.

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