Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations

Abstract

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations of a linear algebraic group.

26 pages; corrected misprints; simplified Definition 2; more references added

References in corpus (2)

• Differential Tannakian Categories
• Tannakian approach to linear differential algebraic groups

Cited by in corpus (14)

• Parameterized Picard-Vessiot extensions and Atiyah extensions
• Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations
• Isomonodromic differential equations and differential categories
• Zariski Closures of Reductive Linear Differential Algebraic Groups
• Differential Tannakian Categories
• Unipotent differential algebraic groups as parameterized differential Galois groups
• Tannakian approach to linear differential algebraic groups
• Extensions of differential representations of SL(2) and tori
• Approche galoisienne de la transcendance différentielle
• Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence
• 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
• Calculating Galois groups of third order linear differential equations with parameters
• Differential Galois Theory of Linear Difference Equations