Generalised Gabriel-Roiter measure and thin representations

Abstract

For Dynkin and Euclidean quivers, it is shown that Gabriel-Roiter measures of thin representations equal the induced chain length functions on the corresponding system of subquivers. This allows a combinatorial procedure to find a GR filtration of thin representations, showing that GR measures of thin representations are field-independent. It is proved that an indecomposable filtration of a thin representation is a GR filtration for a suitable choice of a length function on the category of finite-dimensional representations.

References in corpus (2)

• Ringel-Hall numbers and the Gabriel-Roiter submodules of simple homogeneous regular modules
• The Auslander-Reiten Components in the Rhombic Picture