2024/05/05 by Yuehui Zhang, Zhang, Yuehui, Xiaoqiu Zhong +1 · 1 citation
Computer Science · Mathematics · #16G20 16G10 16D10 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2405.02860
openalex publication_date 2024/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be an algebra with iso-class of simple modules S of cardinality n. A total ordering on S making every Weyl module Schurian and every indecomposable projective module filtered by the Weyl modules is called to be a quasi-hereditary ordering or q-ordering on A and A is a quasi-hereditary algebra under this ordering. The number of q-orderings on A is denoted by q(A). To determine whether an ordering on S is a q-ordering is a hard problem. A famous result due to Dlab and Ringel is that A is hereditary if and only if every ordering is a q-ordering, equivalently, q(A)=n!. The twenty-years old q-ordering conjecture claims that q(A)≤\dfrac23n!. The present paper proves a very simple criterion for q-orderings when A is a Nakayama algebra. This criterion is applied to getting a full classification of all q-orderings of A and an explicit iteration formula for q(A), and also a positive proof of the q-ordering conjecture for Nakayama algebras.