2024/08/07 by Bohan Xing, Xing, Bohan
Computer Science · Mathematics · #16D40 #16D50 #16G20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2408.03778
openalex publication_date 2024/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Biserial algebras are a classical class in the representation theory of algebras, generalizing Nakayama algebras. They were further generalized by Green and Schroll to multiserial algebras, which share many structural properties with biserial algebras. Inspired by their motivation, we introduce another generalization, called quasi-biserial algebras. We show that this class retains fundamental properties of classical biserial algebras. In the symmetric special case, we establish a correspondence with labeled ribbon graphs equipped with multiplicities, providing a combinatorial model for the algebras. Furthermore, we prove that Kauer moves on these graphs, interpreted as mutations of labeled ribbon graphs, induce derived equivalences between the associated symmetric special quasi-biserial algebras.