Abstract
A differential central simple algebra, and in particular a differential matrix algebra, over a differential field K with constants C can be trivialized by a Picard-Vessiot (differential Galois) extension E. In the matrix algebra case, there is a correspondence between K-algebras trivialized by E and representations of the Galois group of E over K in PGL n (C), which can be interpreted as cocyles equivalent up to coboundaries.
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