Differential Tannakian Categories

Mathematics – Representation Theory

Scientific paper

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

Scientific paper

10.1016/j.jalgebra.2009.02.008

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.

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