Some Remarks on Dirac Structures and Poisson Reductions

• Autorzy: Zhang-Ju Liu
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 51
• Numer: 1
• Strony: 165-173

Daty

wydano

2000

Twórcy

autor

Zhang-Ju Liu

• Department of Mathematics, Peking University, Beijing, 100871, China

Bibliografia

• [1] A. Alekseev and Y. Kosmann-Schwarzbach, Manin pairs and moment maps, preprint.
• [2] T. J. Courant, Dirac manifolds, Trans. A.M.S. 319 (1990), 631-661.
• [3] A. Diatta and A. Medina, Poisson homogeneous spaces of a Poisson Lie group, preprint.
• [4] T. Kimura, Generalized classical BRST cohomology and reduction of Poisson manifolds, Commun. Math. Phys. 151 (1993), 155-182.
• [5] Y. Kosmann-Schwarzbach, Exact Gerstenhaber algebras and Lie bialgebroids, Acta Appl. Math. 41 (1995), 153-165.
• [6] Z.-J. Liu, A. Weinstein and P. Xu, Manin triples for Lie bialgebroids, J. Diff. Geom. 45 (1997), 547-574.
• [7] Z.-J. Liu, A. Weinstein and P. Xu, Dirac structures and Poisson homogeneous spaces, Commun. Math. Phys. 192 (1998), 121-144.
• [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.
• [9] K. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Math. J. 18 (1994), 415-452.
• [10] J. E. Marsden and T. Ratiu, Reduction of Poisson manifolds, Lett. Math. Phys. 11 (1986), 161-169.
• [11] K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoid actions, Publ. RIMS Kyoto Univ. 24 (1988), 121-140.
• [12] J. Stasheff, Homological reduction of constrained Poisson algebras, J. Diff. Geom. 45 (1997), 221-240.
• [13] A. Weinstein, Coisotropic calculus and Poisson groupoids, J. Math. Soc. Japan 40 (1988), 705-727.