Quasi-biserial algebras, special quasi-biserial algebras and symmetric fractional Brauer graph algebras

Abstract: This paper develops the theory of quasi-biserial and special quasi-biserial algebras, relating them to symmetric fractional Brauer graph algebras. We prove that these algebras generalize key properties of classical biserial algebras, and establish that symmetric special quasi-biserial algebras are exactly those determined by combinatorial data (a labeled ribbon graph with a multiplicity function). Furthermore, we show that Kauer moves on labeled ribbon graphs induce derived equivalences between the corresponding symmetric special quasi-biserial algebras.