2022/08/15 by J. M. Chen, Chen, J. M., J. Y. Chen +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2208.06978
openalex publication_date 2022/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Frobenius-Perron dimension of representation-directed algebras and quotient algebras of canonical algebras of type ADE, prove that the Frobenius-Perron dimension of a representation-directed algebra is always zero and the Frobenius-Perron dimension of a quotient algebra of canonical algebras of type ADE is 0 or 1. Moreover, we give a sufficient and necessary condition for a quotient algebra of a canonical algebra of type ADE under which its Frobenius-Perron dimension is 0.