Dirac structures are characterized in terms of their characteristic pairs defined in this note and then Poisson reductions are discussed from the point of view of Dirac structures.
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p165bwm, author = {Liu, Zhang-Ju}, title = {Some Remarks on Dirac Structures and Poisson Reductions}, journal = {Banach Center Publications}, volume = {51}, year = {2000}, pages = {165-173}, zbl = {0966.58013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p165bwm} }
Liu, Zhang-Ju. Some Remarks on Dirac Structures and Poisson Reductions. Banach Center Publications, Tome 51 (2000) pp. 165-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p165bwm/
[000] [1] A. Alekseev and Y. Kosmann-Schwarzbach, Manin pairs and moment maps, preprint.
[001] [2] T. J. Courant, Dirac manifolds, Trans. A.M.S. 319 (1990), 631-661. | Zbl 0850.70212
[002] [3] A. Diatta and A. Medina, Poisson homogeneous spaces of a Poisson Lie group, preprint. | Zbl 0955.53045
[003] [4] T. Kimura, Generalized classical BRST cohomology and reduction of Poisson manifolds, Commun. Math. Phys. 151 (1993), 155-182. | Zbl 0768.58016
[004] [5] Y. Kosmann-Schwarzbach, Exact Gerstenhaber algebras and Lie bialgebroids, Acta Appl. Math. 41 (1995), 153-165. | Zbl 0837.17014
[005] [6] Z.-J. Liu, A. Weinstein and P. Xu, Manin triples for Lie bialgebroids, J. Diff. Geom. 45 (1997), 547-574. | Zbl 0885.58030
[006] [7] Z.-J. Liu, A. Weinstein and P. Xu, Dirac structures and Poisson homogeneous spaces, Commun. Math. Phys. 192 (1998), 121-144. | Zbl 0921.58074
[007] [8] J.-H. Lu, Momentum mappings and reductions of Poisson actions, in: Symplectic Geometry, Groupoids and Integrable Systems, P. Dazord and A. Weinstein, eds., Springer-Verlag 1991, 209-226. | Zbl 0735.58004
[008] [9] K. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Math. J. 18 (1994), 415-452. | Zbl 0844.22005
[009] [10] J. E. Marsden and T. Ratiu, Reduction of Poisson manifolds, Lett. Math. Phys. 11 (1986), 161-169. | Zbl 0602.58016
[010] [11] K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoid actions, Publ. RIMS Kyoto Univ. 24 (1988), 121-140. | Zbl 0659.58016
[011] [12] J. Stasheff, Homological reduction of constrained Poisson algebras, J. Diff. Geom. 45 (1997), 221-240. | Zbl 0874.58020
[012] [13] A. Weinstein, Coisotropic calculus and Poisson groupoids, J. Math. Soc. Japan 40 (1988), 705-727. | Zbl 0642.58025