2015/07/27 by Shulim Kaliman, Frank Kutzschebauch, Kaliman, Shulim +1
Mathematics · #14R20 Secondary: 14R10 #32M25 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Primary: 32M05 #math.AG #math.CV #msc:14R10 #msc:14R20 #msc:32M05 #msc:32M25
paper · pdf · doi:10.48550/arxiv.1507.07604
21 pages
arxiv created 2015/07/27 · arxiv updated 2015/08/02
Let X be a connected affine homogenous space of a linear algebraic group G over \C. (1) If X is different from a line or a torus we show that the space of all algebraic vector fields on X coincides with the Lie algebra generated by complete algebraic vector fields on X. (2) Suppose that X has a G-invariant volume form ω. We prove that the space of all divergence-free (with respect to ω) algebraic vector fields on X coincides with the Lie algebra generated by divergence-free complete algebraic vector fields on X (including the cases when X is a line or a torus). The proof of these results requires new criteria for algebraic (volume) density property based on so called module generating pairs.