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- W4299600369 abstract "We give a complete classification of the infinite dimensional tilting modules over a tame hereditary algebra R. We start our investigations by considering tilting modules of the form T=R_Uoplus R_U /R where U is a union of tubes, and R_U denotes the universal localization of R at U in the sense of Schofield and Crawley-Boevey. Here R_U/R is a direct sum of the Prufer modules corresponding to the tubes in U. Over the Kronecker algebra, large tilting modules are of this form in all but one case, the exception being the Lukas tilting module L whose tilting class Gen L consists of all modules without indecomposable preprojective summands. Over an arbitrary tame hereditary algebra, T can have finite dimensional summands, but the infinite dimensional part of T is still built up from universal localizations, Prufer modules and (localizations of) the Lukas tilting module. We also recover the classification of the infinite dimensional cotilting R-modules due to Buan and Krause." @default.
- W4299600369 created "2022-10-02" @default.
- W4299600369 creator A5052612855 @default.
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- W4299600369 date "2010-07-23" @default.
- W4299600369 modified "2023-09-25" @default.
- W4299600369 title "Tilting Modules over Tame Hereditary Algebras" @default.
- W4299600369 doi "https://doi.org/10.48550/arxiv.1007.4233" @default.
- W4299600369 hasPublicationYear "2010" @default.
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