Reduction of local Lie algebra structures

Reduction of local Lie algebra structures
HTML articles powered by AMS MathViewer

by Kentaro Mikami PDF

Proc. Amer. Math. Soc. 105 (1989), 686-691 Request permission

We deal with the reduction theory of local Lie algebra structures in the function space through coadjoint equivariant momentum mappings.

References

Le théorème de réduction de Marsden-Weinstein pour les structures de contact

A. A. Kirillov, Local Lie algebras, Uspehi Mat. Nauk 31 (1976), no. 4(190), 57–76 (Russian). MR 0438390
Jerrold E. Marsden and Tudor Ratiu, Reduction of Poisson manifolds, Lett. Math. Phys. 11 (1986), no. 2, 161–169. MR 836071, DOI 10.1007/BF00398428
Jerrold Marsden and Alan Weinstein, Reduction of symplectic manifolds with symmetry, Rep. Mathematical Phys. 5 (1974), no. 1, 121–130. MR 402819, DOI 10.1016/0034-4877(74)90021-4
Kentaro Mikami, Local Lie algebra structure and momentum mapping, J. Math. Soc. Japan 39 (1987), no. 2, 233–246. MR 879926, DOI 10.2969/jmsj/03920233
Alan Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), no. 3, 523–557. MR 723816