Mathematical Research Letters

Volume 16, Issue 2, March 2009 pp. 215-232.

Courant morphisms and moment maps

Authors: Henrique Bursztyn (1), David Iglesias Ponte (2), and Pavol Severa (3)
Author institution: Instituto Nacional de Matemática Pura e Aplicada (1), Instituto de Ciencias Matemáticas (2), and Université de Genève (3)

Summary: 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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