Galois coverings of selfinjective algebras by repetitive algebras
Trans. Amer. Math. Soc. 351 (1999), pp. 715-734 
Andrzej Skowronski 
Faculty of Mathematics and Informatics, Nicholas Copernicus University, 
Chopina 12/18, 87-100 Torun, Poland 
and Kunio Yamagata
Department of Mathematics, Tokyo University of Agriculture and Technology, 
Fuchu, Tokyo 183, Japan 

Abstract. In the representation theory of selfinjective artin algebras an 
important role is played by selfinjective algebras of the form $\hat B/G$ 
where $\hat B$ is the repetitive algebra of an artin algebra $B$ and $G$
is an admissible group of automorphisms of $\hat B$. If $B$ finite global 
dimension, then the stable module category $\underline{\text{\rm mod}}\hat B$ 
of finitely generated $\hat B$-modules is equivalent to the derived category 
$D^b(\text{\rm mod} B)$ of bounded complexes of finitely generated 
$B$-modules. For a selfinjective artin algebra $A$, an ideal $I$ and $B = A/I$,
we establish a criterion for $A$ to admit a Galois covering $F : \hat B
\rightarrow \hat B/G = A$ with an infinite cyclic Galois group $G$. As an 
application we prove that all selfinjective artin algebras $A$ whose 
Auslander-Reiten quiver $\Gamma_A$ has a non-periodic generalized standard 
translation subquiver closed under successors in $\Gamma_A$ are socle 
equivalent to the algebras $\hat B/G$, where $B$ is a representation-infinite 
tilted algebra and $G$ is an infinite cyclic group of automorphisms of 
$\hat B$.