Some Remarks on Dirac Structures and Poisson Reductions

Zhang-Ju Liu

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 165-173
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Liu, Zhang-Ju. "Some Remarks on Dirac Structures and Poisson Reductions." Banach Center Publications 51.1 (2000): 165-173. <http://eudml.org/doc/209028>.

@article{Liu2000,
abstract = {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.},
author = {Liu, Zhang-Ju},
journal = {Banach Center Publications},
keywords = {Dirac structures; Lie bialgebroids; Poisson reductions},
language = {eng},
number = {1},
pages = {165-173},
title = {Some Remarks on Dirac Structures and Poisson Reductions},
url = {http://eudml.org/doc/209028},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Liu, Zhang-Ju
TI - Some Remarks on Dirac Structures and Poisson Reductions
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 165
EP - 173
AB - 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.
LA - eng
KW - Dirac structures; Lie bialgebroids; Poisson reductions
UR - http://eudml.org/doc/209028
ER -

References

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  1. [1] A. Alekseev and Y. Kosmann-Schwarzbach, Manin pairs and moment maps, preprint. 
  2. [2] T. J. Courant, Dirac manifolds, Trans. A.M.S. 319 (1990), 631-661. Zbl0850.70212
  3. [3] A. Diatta and A. Medina, Poisson homogeneous spaces of a Poisson Lie group, preprint. Zbl0955.53045
  4. [4] T. Kimura, Generalized classical BRST cohomology and reduction of Poisson manifolds, Commun. Math. Phys. 151 (1993), 155-182. Zbl0768.58016
  5. [5] Y. Kosmann-Schwarzbach, Exact Gerstenhaber algebras and Lie bialgebroids, Acta Appl. Math. 41 (1995), 153-165. Zbl0837.17014
  6. [6] Z.-J. Liu, A. Weinstein and P. Xu, Manin triples for Lie bialgebroids, J. Diff. Geom. 45 (1997), 547-574. Zbl0885.58030
  7. [7] Z.-J. Liu, A. Weinstein and P. Xu, Dirac structures and Poisson homogeneous spaces, Commun. Math. Phys. 192 (1998), 121-144. Zbl0921.58074
  8. [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. Zbl0735.58004
  9. [9] K. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Math. J. 18 (1994), 415-452. Zbl0844.22005
  10. [10] J. E. Marsden and T. Ratiu, Reduction of Poisson manifolds, Lett. Math. Phys. 11 (1986), 161-169. Zbl0602.58016
  11. [11] K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoid actions, Publ. RIMS Kyoto Univ. 24 (1988), 121-140. Zbl0659.58016
  12. [12] J. Stasheff, Homological reduction of constrained Poisson algebras, J. Diff. Geom. 45 (1997), 221-240. Zbl0874.58020
  13. [13] A. Weinstein, Coisotropic calculus and Poisson groupoids, J. Math. Soc. Japan 40 (1988), 705-727. Zbl0642.58025

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