Abstract
According to a result claimed by Pogorza_ly, selfinjective special biserial algebras can be stably equivalent to stably biserial algebras only, and these two classes coincide. By an example of Ariki, Iijima, and Park, the classes of stably biserial and selfinjective special biserial algebras do not coincide. In these notes based on some ideas from the Pogorzaly paper, a detailed proof is given for the fact that a selfinjective special biserial algebra can be stably equivalent to a stably biserial algebra only. The structure of symmetric stably biserial algebras is analyzed. It is shown that in characteristic other than 2, the classes of symmetric special biserial (Brauer graph) algebras and symmetric stably biserial algebras coincide. Also a proof of the Auslander–Reiten conjecture for special biserial algebras is given.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
