Csaba Szántó (Cluj)

Ringel-Hall polynomials and Gabriel-Roiter measure over Euclidean quivers.

Abstract:

Bo Chen's theorem in the Dynkin case states that if T is a Gabriel-Roiter submodule of M then Hom(T,M/T)=0 (all modules being indecomposable). Ringel proved this theorem comparing all possible Ringel-Hall polynomials (involving only indecomposables) with the special form they take in case of a Gabriel-Roiter inclusion. We will implement Ringel's idea in the Euclidean quiver context obtaining some new results on Gabriel-Roiter inclusions. For this purpose we have also determined a list of special Ringel-Hall polynomials in the Euclidean case which may have further applications.