Courant morphisms and moment maps

• Autores: Henrique Bursztyn, David Iglesias Ponte , Pavol Severa
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 2-3, 2009, págs. 215-232
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n2.a2
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• Resumen

  • 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.