Transitive Subgroups of Transvections Acting on Some Symplectic Symmetric Spaces of Ricci Type

Abstract

Symmetric symplectic spaces of Ricci type are a class of symmetric symplectic spaces which can be entirely described by reduction of certain quadratic Hamiltonian systems in a symplectic vector space. We determine, in a large number of cases, if such a space admits a subgroup of its transvection group acting simply transitively. We observe that the simply transitive subgroups obtained are one dimensional extensions of the Heisenberg group.

References in corpus (4)

• Generalized Kahler and hyper-Kahler quotients
• Non-formal deformation quantizations of solvable Ricci-type symplectic symmetric spaces
• Quantized anti de Sitter spaces and non-formal deformation quantizations of symplectic symmetric spaces
• Symplectic Symmetric Spaces