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We describe the structure of finite-dimensional algebras of domestic representation type over an algebraically closed field whose Auslander-Reiten quiver consists of generalized standard and semiregular components. Moreover, we prove that this class of algebras contains all special biserial algebras whose Auslander-Reiten quiver consists of semiregular components.

Abstract. We describe the structure of finite dimensional selfinjective algebras over an arbitrary field without short cycles of indecomposable modules.Keyword: selfinjective algebra, repetitive algebra, orbit algebra, tilted algebra, algebra of finite representation type, short cycle of modules 2010 MSC: 16D50, 16G10, 16G60, 16G70Introduction and the main result.

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