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

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

2010-10-14

arxiv.org/abs/1010.2900v1

Mathematics

Symplectic Geometry

Scientific paper

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.

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