A Universal Reduction Procedure for Hamiltonian Group Actions ∗

@inproceedings{Arms1991AUR,
  title={A Universal Reduction Procedure for Hamiltonian Group Actions ∗},
  author={Judith M. Arms and Richard H. Cushman and Mark J. Gotay},
  year={1991}
}
We give a universal method of inducing a Poisson structure on a singular reduced space from the Poisson structure on the orbit space for the group action. For proper actions we show that this reduced Poisson structure is nondegenerate. Furthermore, in cases where the Marsden-Weinstein reduction is well-defined, the action is proper, and the preimage of a coadjoint orbit under the momentum mapping is closed, we show that universal reduction and Marsden-Weinstein reduction coincide. As an example… CONTINUE READING
Highly Influential
This paper has highly influenced 13 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 91 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.

91 Citations

0510'93'98'04'10'16
Citations per Year
Semantic Scholar estimates that this publication has 91 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 30 references

Singularités C∞ en présence de symétrie

V. Poènaru
Lect. Notes in Math., • 1976
View 4 Excerpts
Highly Influenced

On the existence of slices for actions of non-compact Lie groups

R. Palais
Ann. Math., • 1961
View 5 Excerpts
Highly Influenced

Reduction and quantization for singular momentum mappings

J. Śniatycki, A. Weinstein
Lett. Math. Phys., • 1983
View 15 Excerpts
Highly Influenced

Reduction of symplectic manifolds with symmetry

J. Marsden, A. Weinstein
Rep. Math. Phys., • 1974
View 14 Excerpts
Highly Influenced

The classical groups, 2 ed

H. Weyl
1946
View 3 Excerpts
Highly Influenced

Computing invariants, Lect

G. Kempf
Notes in Math., • 1987
View 1 Excerpt

On resonant Hamiltonian systems with finitely many degrees of freedom

M. Kummer
Lect . Notes in Phys . • 1986

On resonant Hamiltonian systems with finitely many degrees of freedom, Lect

M. Kummer
Notes in Phys., • 1986
View 1 Excerpt

Realizations of the reduced phase space of a Hamiltonian system with symmetry

M. Kummer
Lect . Notes in Phys . • 1986

Realizations of the reduced phase space of a Hamiltonian system with symmetry, Lect

M. Kummer
Notes in Phys., • 1986
View 1 Excerpt

Similar Papers

Loading similar papers…