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Selfinjective biserial standard algebras. (English) Zbl 0808.16019

Throughout the paper, \(K\) will denote a fixed algebraically closed field. By an algebra \(A\) is meant an associative, finite-dimensional \(K\)-algebra with an identity, which we shall assume to be basic and connected. An algebra \(A\) is called biserial if the radical of any indecomposable nonuniserial projective, left or right, \(A\)-module is a sum of at most two uniserial submodules whose intersection is simple or zero. In this article, with the help of Galois covers, we describe all representation- infinite standard selfinjective biserial algebras. The covers used here are constructed from locally bounded tree \(K\)-categories whose finite full convex subcategories are iterated tilted categories of type \(A_ n\). In particular, we obtain that the class of selfinjective special biserial algebras coincides with the class of selfinjective standard biserial algebras.

MSC:

16G60 Representation type (finite, tame, wild, etc.) of associative algebras
16G30 Representations of orders, lattices, algebras over commutative rings
16D50 Injective modules, self-injective associative rings
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