Picard-Vessiot Extensions For Unipotent Algebraic Groups

2011/02/15 by Varadharajan Srinivasan, V. Ravi Srinivasan, Srinivasan, V. Ravi
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Polynomial and algebraic computation #math.CA

paper · pdf · doi:10.48550/arxiv.1102.3205

arxiv created 2011/02/15 · openalex publication_date 2011/02/15 · arxiv updated 2011/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a differential field of characteristic zero. In this article, we construct Picard-Vessiot extensions of F whose differential Galois group is isomorphic to the full unipotent subgroup of the upper triangular group defined over the field of constants of F. We will also give a procedure to compute linear differential operators for our Picard-Vessiot extensions. We do not require the condition that the field of constants be algebraically closed.

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