Galois coverings of selfinjective algebras by repetitive algebras

In the representation theory of selfinjective artin algebras an important r ole is played by selfinjective algebras of the form (B) over cap/G where (B ) over cap is the repetitive algebra of an artin algebra B and G is an admi ssible group of automorphisms of (B) over cap. If B is of finite global dim ension, then the stable module category mod (B) over cap of finitely genera ted (B) over cap-modules is equivalent to the derived category D-b(mod B) o f bounded complexes of finitely generated B-modules. For a selfinjective ar tin algebra A, an ideal I and B = A/I, we establish a criterion for A to ad mit a Galois covering F : (B) over cap --> (B) over cap/G = A with an infin ite cyclic Galois group G. As an application we prove that all selfinjectiv e artin algebras A whose Auslander-Reiten quiver Gamma(A) has a non-periodi c generalized standard translation subquiver closed under successors in Gam ma(A) are socle equivalent to the algebras (B) over cap/G, where B is a rep resentation-infinite tilted algebra and G is an infinite cyclic group of au tomorphisms of (B) over cap.