带有正则单模的Nakayama代数的计数
Counting Nakayama Algebras with Regular Simple Modules
DOI: 10.12677/pm.2025.154128, PDF,   
作者: 纪文昶：上海理工大学理学院，上海
关键词: Nakayama代数；Dyck路；正则单模；Nakayama Algebras； Dyck Paths； Regular Simple Modules
摘要: 有限生成投射模范畴的正合结构的分类与2正则单模有关。基于Nakayama代数上的正则单模的代数性质与Dyck路的组合结构的对应，计算了带有k个1正则单模(或k个2正则单模)的(n + 1)-LNakayama代数和拟遗传n-CNakayama代数的个数。
Abstract: The classification of exact structures in the category of finitely generated projective modules for finite dimensional algebras were reduced to the classification of 2-regular simple modules. By the result of relations between regular simple modules over Nakayama algebras and certain combinatorial structures of Dyck paths, the number of (n + 1)-LNakayama algebras and quasi-hereditary n-CNakayama algebras that have exactly k 1-regular simple modules (respectively k 2-regular simple modules) was calculated.
文章引用：纪文昶. 带有正则单模的Nakayama代数的计数[J]. 理论数学, 2025, 15(4): 257-265. https://doi.org/10.12677/pm.2025.154128

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