Tannakian Categories and Linear Differential Algebraic Groups

Please use this identifier to cite or link to this item: http://www.lib.ncsu.edu/resolver/1840.16/4801

Title:	Tannakian Categories and Linear Differential Algebraic Groups
Authors:	Ovchinnikov, Alexey
Advisors:	Irina Kogan, Committee Member Bojko Bakalov, Committee Member Kailash Misra, Committee Member Michael Singer, Committee Chair
Keywords:	Galois theory of differential equations differential algebraic groups tannakian categories
Issue Date:	28-Feb-2007
Degree:	PhD
Discipline:	Mathematics
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.
URI:	http://www.lib.ncsu.edu/resolver/1840.16/4801
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