2023/02/02 by Yuichiro Goto, Goto, Yuichiro
Computer Science · Mathematics · #16G20 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2302.00831
openalex publication_date 2023/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dlab and Ringel showed that algebras being quasi-hereditary in all total orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary. As a matter of fact, we consider permutations of indices instead of total orders. If the standard modules defined by two permutations coincide, we say that the permutations are equivalent. Moreover if the algebra with permuted indices is quasi-hereditary, then this equivalence class of the permutation is called a quasi-hereditary structure. In this article, we give a method of counting the number of quasi-hereditary structures for certain algebras.