A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group G on the quotient of a Poisson G-space P to be a Poisson action, where both the Poisson structures on the quotient gr...A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group G on the quotient of a Poisson G-space P to be a Poisson action, where both the Poisson structures on the quotient group and the quotient manifold are induced by Dirac structures. The left invariant Dirac structure and the left invariant tensor descriptions of Poisson homogeneous spaces are proved to be equivalent.展开更多
A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for t...A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.展开更多
文摘A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group G on the quotient of a Poisson G-space P to be a Poisson action, where both the Poisson structures on the quotient group and the quotient manifold are induced by Dirac structures. The left invariant Dirac structure and the left invariant tensor descriptions of Poisson homogeneous spaces are proved to be equivalent.
文摘A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.
