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arXiv · 2102.01584

Boundary Idempotents and $2$-precluster-tilting categories

Jordan McMahon
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Abstract

The homological theory of Auslander-Platzeck-Todorov on idempotent ideals laid much of the groundwork for higher Auslander-Reiten theory, providing the key technical lemmas for both higher Auslander correspondence as well as the construction of higher Nakayama algebras, among other results. Given a finite-dimensional algebra $A$ and idempotent $e$, we expand on a criterion of Jasso-K\"ulshammer in order to determine a correspondence between the $2$-precluster-tilting subcategories of $\mathrm{mod}(A)$ and $\mathrm{mod}(A/\langle e\rangle)$. This is then applied in the context of generalising dimer algebras on surfaces with boundary idempotent.

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Jordan McMahon. 2021-02-02. Boundary Idempotents and $2$-precluster-tilting categories. https://arxiv.org/abs/2102.01584

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