Tannakian Categories and Linear Differential Algebraic Groups
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Date
2007-02-28
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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. We also 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.
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Galois theory of differential equations, differential algebraic groups, tannakian categories
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Degree
PhD
Discipline
Mathematics
