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arXiv · 2105.05830

$n$-cluster tilting subcategories for radical square zero algebras

Laertis Vaso
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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 $Q$.

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Laertis Vaso. 2021-05-12. $n$-cluster tilting subcategories for radical square zero algebras. https://arxiv.org/abs/2105.05830

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