Journal of the
Korean Mathematical Society JKMS

If an Azumaya algebra $A$ is a homomorphic image of a finite group ring $RG$ where $G$ is a direct product of subgroups then $A$ can be decomposed into subalgebras $A_i$ which are homomorphic images of subgroup rings of $RG$. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that $A$ is represented by Azumaya group ring $RG$, we study relationships between the representing groups for $A$ and $A_i$.

Keywords: Azumaya algebra, Schur algebra, projective Schur algebra

MSC numbers: 16H05, 16S34, 20C