Tannakian Categories and Linear Differential Algebraic Groups

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Title: Tannakian Categories and Linear Differential Algebraic Groups
Author: Ovchinnikov, Alexey
Advisors: Irina Kogan, Committee Member
Bojko Bakalov, Committee Member
Kailash Misra, Committee Member
Michael Singer, Committee Chair
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.
Date: 2007-02-28
Degree: PhD
Discipline: Mathematics
URI: http://www.lib.ncsu.edu/resolver/1840.16/4801


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