## Abstract

We characterize the principal differential ideals of a polynomial ring in n^{2} indeterminates with coefficients in the ring of differential polynomials in n^{2} indeterminates and derivation given by a "general" element of Lie(GL_{n}) and use this characterization to construct a generic Picard-Vessiot extension for GL_{n}. In the case when the differential base field has finite transcendence degree over its field of constants we provide necessary and sufficient conditions for solving the inverse differential Galois problem for these groups via specialization from our generic extension.

Original language | English |
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Pages (from-to) | 6071-6103 |

Number of pages | 33 |

Journal | Communications in Algebra |

Volume | 30 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2002 |

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