Indecomposable representations of orders
Various results on the induced representations of group rings are extended to modules over strongly group-graded rings. In particular, a proof of the graded version of Mackey's theorem is given.
In this paper we study the precise relation between two representations of a given split finite basic dimensional algebra A as a factor of the free path algebra over its quiver (A). After defining the notion of strongly acyclic quiver, we apply the results obtained to develop a method of calculating the group Aut(A)/Inn(A) in the case when (A) is strongly acyclic.