### Abstract

Let X be a connected affine homogenous space of a linear algebraic group G over (Formula presented.). (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 (Formula presented.). We prove that the space of all divergence-free (with respect to (Formula presented.)) 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Mathematische Annalen |

DOIs | |

State | Accepted/In press - Aug 2 2016 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Annalen*, 1-22. https://doi.org/10.1007/s00208-016-1451-9

**Algebraic (volume) density property for affine homogeneous spaces.** / Kaliman, Shulim; Kutzschebauch, Frank.

Research output: Contribution to journal › Article

*Mathematische Annalen*, pp. 1-22. https://doi.org/10.1007/s00208-016-1451-9

}

TY - JOUR

T1 - Algebraic (volume) density property for affine homogeneous spaces

AU - Kaliman, Shulim

AU - Kutzschebauch, Frank

PY - 2016/8/2

Y1 - 2016/8/2

N2 - Let X be a connected affine homogenous space of a linear algebraic group G over (Formula presented.). (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 (Formula presented.). We prove that the space of all divergence-free (with respect to (Formula presented.)) 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.

AB - Let X be a connected affine homogenous space of a linear algebraic group G over (Formula presented.). (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 (Formula presented.). We prove that the space of all divergence-free (with respect to (Formula presented.)) 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.

UR - http://www.scopus.com/inward/record.url?scp=84982814941&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982814941&partnerID=8YFLogxK

U2 - 10.1007/s00208-016-1451-9

DO - 10.1007/s00208-016-1451-9

M3 - Article

AN - SCOPUS:84982814941

SP - 1

EP - 22

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

ER -