Quasi-biserial algebras, special quasi-biserial algebras and labeled Brauer graph algebras

Abstract

In this paper, we define and study quasi-biserial algebras, special quasi-biserial algebras and labeled Brauer graph algebras. These algebras naturally generalize biserial and special biserial algebras to algebras of wild representation type, in a different direction of multiserial and special multiserial algebras. We show that all special quasi-biserial algebras are quasi-biserial, all special quasi-biserial algebras are quotients of symmetric special quasi-biserial algebras and all symmetric special quasi-biserial algebras are labeled Brauer graph algebras. Moreover, we show that the labeled Brauer graph algebras are derived equivalent under Kauer moves.