Cluster algebras and semipositive symmetrizable matrices

Ahmet Seven

There is a close relationship between cluster algebras and symmetrizable matrices. It is known, by the work of Barot-Geiss-Zelevinsky, that finite type cluster algebras are in a natural correspondence with a class of positive symmetrizable matrices called quasi-Cartan matrices. In this talk, we will discuss an extension of this correspondence to semipositive matrices. More specifically, we will give an explicit description of mutation classes of extended Dynkin diagrams and discuss applications.