English

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.

Keywords

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

R2 v1 2026-06-21T10:01:46.244Z