The universal covering and covered spaces of a symplectic Lie algebra action
نویسندگان
چکیده
We show that the category of Hamiltonian covering spaces of a given connected and paracompact symplectic manifold (M, ω) acted canonically upon by a Lie algebra admits a universal covering and covered space.
منابع مشابه
Maximal prehomogeneous subspaces on classical groups
Suppose $G$ is a split connected reductive orthogonal or symplectic group over an infinite field $F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is the Lie algebra of the unipotent radical $N.$ Under the adjoint action of its stabilizer in $M,$ every maximal prehomogeneous subspaces of $frak{n}$ is determined.
متن کاملCompact Symmetric Spaces, Triangular Factorization, and Poisson Geometry
LetX be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X , and let g denote the complexification of the Lie algebra of U , g = u. Each u-compatible triangular decomposition g = n − + h + n+ determines a Poisson Lie group structure πU on U . The Evens-Lu construction ([EL]) produces a (U, πU )-homoge...
متن کاملFiber bundles and Lie algebras of top spaces
In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.
متن کاملHomogeneous symplectic manifolds of Poisson-Lie groups
Symplectic manifolds which are homogeneous spaces of Poisson-Lie groups are studied in this paper. We show that these spaces are, under certain assumptions, covering spaces of dressing orbits of the Poisson-Lie groups which act on them. The effect of the Poisson induction procedure on such spaces is also examined, thus leading to an interesting generalization of the notion of homogeneous space....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006