Algebraic density property of homogeneous spaces

Abstract

Let $X$ be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that $X$ is equipped with several non-degenerate fixed point free $S{L}_2$-actions satisfying some mild additional assumption. Then we show 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 its proper reductive subgroup.

26 pages

References in corpus (3)

• Criteria for the density property of complex manifolds
• Holomorphic DIffeomorphisms of Semisimple Homogeneous Spaces
• Infinite-dimensionality of the Automorphism Groups of Homogeneous Stein Manifolds