Differential Tannakian Categories

Abstract

We define a differential Tannakian category and show that under a natural assumption it has a fibre functor. If in addition this category is neutral, that is, the target category for the fibre functor are finite dimensional vector spaces over the base field, then it is equivalent to the category of representations of a (pro-)linear differential algebraic group. Our treatment of the problem is via differential Hopf algebras and Deligne's fibre functor construction.

24 pages; better structured Definition 2 and other statements of the paper; more examples; more detailed proof of Theorem 14

References in corpus (2)

• Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations
• Tannakian approach to linear differential algebraic groups

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• Approche galoisienne de la transcendance différentielle
• Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence
• Finiteness properties of affine difference algebraic groups
• Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation
• Computing differential Galois groups of second-order linear $q$-difference equations
• Intrinsic approach to Galois theory of q-difference equations, with the preface to Part 4 "The Galois D-groupoid of a q-difference system'' by Anne Granier
• Tannakian categories with semigroup actions