Dirac geometry, quasi-Poisson actions and D/G-valued moment maps

摘要: We study Dirac structures associated with Manin pairs (d, g) and give a geometric approach to Hamiltonian spaces D/G-valued moment maps, originally introduced by Alekseev Kosmann-Schwarzbach [3] in terms of quasi-Poisson structures. explain how these two distinct frameworks are related each other, proving that they lead isomorphic categories spaces. stress the connection between viewpoint geometry equivariant differential forms. The paper discusses various examples, including q-Hamiltonian Poisson-Lie group actions, explaining presymplectic groupoids notion “double” context.