Derived dynkin extensions |
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Authors: | Peter Dräxler Amrey Krause |
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Institution: | Fakult?t F?r Mathematik , Universit?t Bielefeld , Po Box 100131, Bielefeld, D-33501, Germany |
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Abstract: | The finite dimensional tame hereditary algebras are associated with the extended Dynkin diagrams. An indecomposable module over such an algebra is either preprojective or preinjective or lies in a family of tubes whose tubular type is the corresponding Dynkin diagram. The study of one-point extensions by simple regular modules in such tubes was initiated in Ri]. We generalise this approach by starting out with algebras which are derived equivalent to a tame hereditary algebra and considering one-point extensions by modules which are simple regular in tubes in the derived category. If the obtained tubular type is again a Dynkin diagram these algebras are called derived Dynkin extensions. Our main theorem says that a representation infinite algebra is derived equivalent to a tame hereditary algebra iff it is an iterated derived Dynkin extension of a tame concealed algebra. As application we get a new proof of a theorem in AS] about domestic tubular branch enlargements which uses the derived category instead of combinatorial arguments. |
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Keywords: | Tame algebras derived categories one-point extension |
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