Minimal projective resolutions (Q2719054)
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scientific article; zbMATH DE number 1597944
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimal projective resolutions |
scientific article; zbMATH DE number 1597944 |
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Minimal projective resolutions (English)
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14 May 2001
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finite dimensional algebras
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path algebras
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minimal projective resolutions
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quivers
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Let \(\Lambda\) be a quotient algebra of a path algebra. The authors present an algorithmic method for constructing a projective resolution of a \(\Lambda\)-module. In the finite dimensional case, a recursive procedure for computing minimal projective resolutions is provided.NEWLINENEWLINENEWLINEThen the Ext-algebra of \(\Lambda\) is studied and a case of the no loop conjecture is proved. The construction resembles earlier resolutions of \textit{S. Eilenberg} [Ann. Math., II. Ser. 64, 328-336 (1956; Zbl 0073.26003)] and \textit{K. Bongartz} [J. Lond. Math. Soc., II. Ser. 28, 461-469 (1983; Zbl 0532.16020)].
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