Lie group actions on compact

Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces

Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology.  Dimension of is called the cohomogeneity of the action of  on . If is a differentiable manifold  of  cohomogeneity one under the action of  a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...

On Minimal, Strongly Proximal Actions of Locally Compact Groups

Minimal, strongly proximal actions of locally compact groups on compact spaces, also known as boundary actions, were introduced by Furstenberg in the study of Lie groups. In particular, the action of a semi-simple real Lie group G on homogeneous spaces G/Q where Q ⊂ G is a parabolic subgroup, are boundary actions. Countable discrete groups admit a wide variety of boundary actions. In this note ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

On ergodic ZZ-actions on Lie groups by automorphisms

In response to a question raised by Halmos in his book on ergodic theory ([10], page 29) it was proved that a locally compact group admits a (bicontinuous) group automorphism acting ergodically (with respect to the Haar measure as a quasiinvariant measure) only if it is compact (see [9] for historical details and a generalisation to affine transformations; see [5] for the case of Lie groups). A...

The Fundamental Group of Symplectic Manifolds with Hamiltonian Lie Group Actions

Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian G action, where G is a connected compact Lie group. Let φ be the moment map. In [12], we proved the following result for G = S action: as fundamental groups of topological spaces, π1(M) = π1(Mred), where Mred is the symplectic quotient at any value of the moment map φ, and = denotes “isomorphic to”. In this paper,...