Nakayama algebras and Fuchsian singularities
| Autor: | Helmut Lenzing, Meltzer Hagen, Shiquan Ruan |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
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| Popis: | This present paper is devoted to the study of a class of Nakayama algebras $N_n(r)$ given by the path algebra of the equioriented quiver $\mathbb{A}_n$ subject to the nilpotency degree $r$ for each sequence of $r$ consecutive arrows. We show that the Nakayama algebras $N_n(r)$ for certain pairs $(n,r)$ can be realized as endomorphism algebras of tilting objects in the bounded derived category of coherent sheaves over a weighted projective line, or in its stable category of vector bundles. Moreover, we classify all the Nakayama algebras $N_n(r)$ of Fuchsian type, that is, derived equivalent to the bounded derived categories of extended canonical algebras. We also provide a new way to prove the classification result on Nakayama algebras of piecewise hereditary type, which have been done by Happel--Seidel before. 33 pages, 2 figures |
| Databáze: | OpenAIRE |
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