Doctor of Philosophy (PHD)
Mathematics (Arts and Sciences)
Date of Defense
First Committee Member
Shulim Kaliman - Committee Chair
Second Committee Member
Bruno De Oliveira - Committee Member
Third Committee Member
Alexander Dvorsky - Committee Member
Fourth Committee Member
Orlando Alvarez - Outside Committee Member
Let X be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that X is equipped with several fixed point free non-degenerate SL_2-actions satisfying some mild additional assumption. Then we prove that the Lie algebra generated by completely integrable algebraic vector fields on X coincides with the set of all algebraic vector fields. In particular, we show that apart from a few exceptions this fact is true for any homogeneous space of form G/R where G is a linear algebraic group and R is a proper reductive subgroup of G.
Luna's Slice Theorem; Compatibility Condition
Donzelli, Fabrizio, "Algebraic Density Property of Homogeneous Spaces" (2009). Open Access Dissertations. 209.