Mathematical Research Letters

Volume 16 (2009)

Number 2

Courant morphisms and moment maps

Pages: 215 – 232



Henrique Bursztyn (Instituto Nacional de Matemática Pura e Aplicada)

David Iglesias Ponte (Instituto de Ciencias Matemáticas)

Pavol Severa (Université de Genève)


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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