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A simple homological characterization of string algebras of finite representation type (2105.02948v1)
Published 6 May 2021 in math.RT and math.KT
Abstract: We prove that among the finite dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the property that the middle term of an arbitrary extension of indecomposable modules has at most two direct factors. On the other hand, we show that non-domestic string algebras are very far from having that property.
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