Triviality of differential Galois cohomology of linear differential algebraic groups |
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Authors: | Andrei Minchenko |
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Affiliation: | Department of Mathematics, University of Vienna, Wien, Austria |
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Abstract: | For a partial differential field K, we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over K is equivalent to K being algebraically, Picard–Vessiot, and linearly differentially closed. This cohomological triviality condition is also known to be equivalent to the uniqueness up to an isomorphism of a Picard–Vessiot extension of a linear differential equation with parameters. |
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Keywords: | Differential Galois theory differential algebraic groups |
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