Investigation into algebraic structure of the category of representations of finite demensional algebras

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The aim of the project is to study algebraic structures of the category of representations of finite dimensional algebras.(1) We studied the stable categories of the algebras with Galois coveings by repetitive algebras, and proved the invariance of the property that a self-injecitve algebra has a Galois covering by the repetitive algebra of a quasi-tilted algebra.(2) We studied non-Frobenius self-injecitve (=quasi-Frobenius) algebras, so that we found a characterization of those algebras and showed an example of non-Frobenius self-injective algebras with arbitrarily large dimension. By this example, we know that the example given by Nakayama in 1939 is the one with the smallest dimension.(3) It is an open problem when an algebra has a preinjective component. We studied the problem for one-point extension algebras. We clarified that the existence of preinjective components of a one-point extension depends on AR-components where summands of the module defining the extension belong.