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Feb 23, 2016 at 23:03 comment added Aurel A sufficient condition is that the cocycle has order $n$, where $n$ is the order of $G$ (and the degree of the corresponding algebra). This condition is also necessary over local and global fields or if $n$ is squarefree, but not in general.
Feb 11, 2016 at 12:21 comment added user1688 I presume you have checked Chapters 14ff in Pierce's book on Associative Algebras?
Feb 11, 2016 at 11:06 history asked Steffen Kionke CC BY-SA 3.0