Skew group algebras of deformed preprojective algebras

Suppose that Q is a finite quiver and G⊆Aut(Q) is a finite group, k is an algebraic closed field whose characteristic does not divide the order of G. For any algebra Λ=kQ/I, where I is an arbitrary ideal of path algebra kQ, we give all the indecomposable ΛG-modules from indecomposable Λ-modules when G is abelian. In particular, we apply this result to the deformed preprojective algebra , and get a reflection functor for the module category of . Furthermore, we construct a new quiver QG and prove that is Morita equivalent to for some η.