2021/02/02 by Jordan McMahon, McMahon, Jordan
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2102.01584
openalex publication_date 2021/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-Külshammer in order to determine a correspondence between the 2-precluster-tilting subcategories of mod(A) and mod(A/⟨ e⟩). This is then applied in the context of generalising dimer algebras on surfaces with boundary idempotent.