I will present a construction of a new class of finite-dimensional algebras with interesting representation theoretic properties: they are symmetric, periodic, have tame representation type and can be realized as endomorphism algebras of cluster-tilting objects in suitable triangulated 2-Calabi-Yau categories. The construction is based upon the combinatorial notion of triangulation quivers, which arise naturally from triangulations of oriented surfaces with marked points and are closely related to ribbon graphs.
This class of algebras contains the algebras of quaternion type introduced and studied by Erdmann with relation to certain blocks of group algebras. On the other hand, it contains also the Jacobian algebras of the quivers with potentials associated by Fomin-Shapiro-Thurston and Labardini to triangulations of closed surfaces with punctures. Hence our construction may serve as a bridge between the modular representation theory of finite groups and the theory of cluster algebras.
All notions will be explained during the talk.