Tannakian approach to linear differential algebraic groups

Abstract

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.

31 pages; corrected misprints

References in corpus (1)

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

Cited by in corpus (12)

• Parameterized Picard-Vessiot extensions and Atiyah extensions
• Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations
• 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
• Galois groups for integrable and projectively integrable linear difference equations
• Extensions of differential representations of SL(2) and tori
• Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence
• Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation
• Tannakian categories with semigroup actions