Jordan-Hölder theorems for derived categories of derived discrete algebras (Q298038)
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scientific article; zbMATH DE number 6595348
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Jordan-Hölder theorems for derived categories of derived discrete algebras |
scientific article; zbMATH DE number 6595348 |
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Jordan-Hölder theorems for derived categories of derived discrete algebras (English)
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20 June 2016
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derived discrete algebra
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\(n\)-derived-simple algebra
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\(n\)-composition-series
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\(n\)-composition-factor
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2-truncated cycle algebra
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Derived discrete algebras were introduced by \textit{D. Vossieck} [J. Algebra 243, No. 1, 168--176 (2001; Zbl 1038.16010)] who classified them into piecewise hereditary algebras of Dynkin type and certain one-cycle gentle algebras. The classification, up to derived equivalence, was improved by\textit{G. Bobiński} et al. [Cent. Eur. J. Math. 2, No. 1, 19--49 (2004; Zbl 1036.18007)].NEWLINENEWLINEIn the paper under review, the author uses the language of \(n\)-recollements, and proves a corresponding Jordan-Hölder theorem for derived discrete algebras. This naturally leads to the consideration of \(n\)-derived-simple objects. A complete classification of \(n\)-derived-simple derived discrete algebras is given up to derived equivalence.
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