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Algebraic density property of homogeneous spaces

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Abstract

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 nondegenerate SL2-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 space 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 closed proper reductive subgroup of G.

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Authors and Affiliations

  1. Institute of Mathematical Sciences, Stony Brook University, Stony Brook, NY, 11794, USA

    F. Donzelli

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    A. Dvorsky & S. Kaliman

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  1. F. Donzelli
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  2. A. Dvorsky
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  3. S. Kaliman
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Correspondence to F. Donzelli.

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Donzelli, F., Dvorsky, A. & Kaliman, S. Algebraic density property of homogeneous spaces. Transformation Groups 15, 551–576 (2010). https://doi.org/10.1007/s00031-010-9091-8

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