n-cluster tilting subcategories for radical square zero algebras

Vaso, Laertis

doi:10.1016/j.jpaa.2022.107157

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n-cluster tilting subcategories for radical square zero algebras

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Vaso, Laertis
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.jpaa.2022.107157
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https://doi.org/10.48550/arXiv.2105.05830
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Citation

Vaso, L. (2023). n-cluster tilting subcategories for radical square zero algebras. Journal of Pure and Applied Algebra, 227(1): 107157. doi:10.1016/j.jpaa.2022.107157.

Cite as: https://hdl.handle.net/21.11116/0000-000A-98F4-7

Abstract

We give a characterization of radical square zero bound quiver algebras
$\mathbf{k} Q/\mathcal{J}^2$ that admit $n$-cluster tilting subcategories and
$n\mathbb{Z}$-cluster tilting subcategories in terms of $Q$. We also show that
if $Q$ is not of cyclically oriented extended Dynkin type $\tilde{A}$, then the
poset of $n$-cluster tilting subcategories of $\mathbf{k} Q/\mathcal{J}^2$ with
relation given by inclusion forms a lattice isomorphic to the opposite of the
lattice of divisors of an integer which depends on $Q$.