Invariant properties of modules under smash products from finite dimensional algebras.

We give the relationship between indecomposable modules over the finite dimensional k-algebra A and the smash product A♯G respectively, where G is a finite abelian group satisfying G ⊆ Aut(A), and k is an algebraically closed field with the characteristic not dividing the order of G. More precisely, we construct all indecomposable A♯G-modules from indecomposable A-modules and prove that an A♯G-module is indecomposable if and only if it is an indecomposable G-stable module over A. Besides, we give the relationship between simple, projective and injective modules in modA and those in modA♯G. [ABSTRACT FROM AUTHOR]