2022/03/29 by Qiang Dong, Dong, Qiang, Yanan Lin +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2203.15735
openalex publication_date 2022/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate the incidence algebras arising from one-branch extensions of "rectangles". There are four different ways to form such extensions, and all four kinds of incidence algebras turn out to be derived equivalent. We provide realizations for all of them by tilting complexes in a Nakayama algebra. As an application, we obtain the explicit formulas of the Coxeter polynomials for a half of Nakayama algebras (i.e., the Nakayama algebras N(n,r) with 2r≥ n+2). Meanwhile, an unexpected derived equivalence between Nakayama algebras N(2r-1,r) and N(2r-1,r+1) has been found.