The role of gentle algebras in higher homological algebra
| Autor: | Sibylle Schroll, Karin Marie Jacobsen, Johanne Haugland |
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| Rok vydání: | 2022 |
| Předmět: |
d-abelian category
18E30 16E35 16G10 Mathematics::Category Theory higher homological algebra Applied Mathematics General Mathematics FOS: Mathematics Representation Theory (math.RT) d-cluster tilting subcategory Mathematics::Representation Theory Mathematics - Representation Theory (d + 2)-angulated category Gentle algebra |
| Zdroj: | Haugland, J, Jacobsen, K M & Schroll, S 2022, ' The role of gentle algebras in higher homological algebra ', Forum Mathematicum, vol. 34, no. 5, pp. 1255-1275 . https://doi.org/10.1515/forum-2021-0311 Forum mathematicum |
| ISSN: | 1435-5337 0933-7741 |
| Popis: | We investigate the role of gentle algebras in higher homological algebra. In the first part of the paper, we show that if the module category of a gentle algebra $\Lambda$ contains a $d$-cluster tilting subcategory for some $d \geq 2$, then $\Lambda$ is a radical square zero Nakayama algebra. This gives a complete classification of weakly $d$-representation finite gentle algebras. In the second part, we use a geometric model of the derived category to prove a similar result in the triangulated setup. More precisely, we show that if $\mathcal{D}^b(\Lambda)$ contains a $d$-cluster tilting subcategory that is closed under $[d]$, then $\Lambda$ is derived equivalent to an algebra of Dynkin type $A$. Furthermore, our approach gives a geometric characterization of all $d$-cluster tilting subcategories of $\mathcal{D}^b(\Lambda)$ that are closed under $[d]$. Comment: Minor changes |
| Databáze: | OpenAIRE |
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