Differential central simple algebras and picard-vessiot representations

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.