Gentle algebras and derived equivalence Diana Avella Alaminos
Matem´aticas
Facultad de Ciencias UNAM
Av. Universidad 3000 Copilco Coyoac´an M´exico DF M´exico
E-mail address:avella@matem.unam.mx
Joint work with Christof Geiss.
We study the classification of gentle algebras according to derived equivalence, which is well under- stood in the case of gentle algebras whose associated quiver has just one cycle.
We define derived equivalent invariants for gentle algebras, constructed in an easy combinatorial way from the quiver with relations defining these algebras. They consist of pairs of natural numbers and contain important information about the algebra and the structure of the stable Auslander-Reiten quiver of its repetitive algebra.
References
[1] D. Avella-Alaminos, C. Geiss, Combinatorial derived invariants for gentle algebras, J. Pure Appl.
Algebra212(2008), no. 1, 228-243.
1