Principal differential ideals and a generic inverse differential galois problem for GLn

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Abstract

We characterize the principal differential ideals of a polynomial ring in n2 indeterminates with coefficients in the ring of differential polynomials in n2 indeterminates and derivation given by a "general" element of Lie(GLn) and use this characterization to construct a generic Picard-Vessiot extension for GLn. 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 languageEnglish
Pages (from-to)6071-6103
Number of pages33
JournalCommunications in Algebra
Volume30
Issue number12
DOIs
StatePublished - Dec 1 2002

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