Courant morphisms and moment maps

Date
Authors
Bursztyn, Henrique
Ponte, David Iglesias
Severa, Pavol
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
Comment: 18 pages. v2: Minor corrections, one example (Example 2.11) added. v3: Remark 2.5 fixed. To appear in Math. Research Letters
Keywords
Mathematics - Symplectic Geometry, Mathematics - Differential Geometry
Citation
Collections