On the combinatorics of the set of tilting modules

摘要

Let A be a basic artin algebra and mod Λ the category of finitely generated left A-modules. We denote by J_Λ the set of all multiplicity free tilting modules over A up to isomorphism. The set J_Λ carries various combinatorial structures. It defines a partially ordered set(J_Λ, ≤), the vertex-set of a quiver and the maximal simplices of a simplicial complex Σ_Λ. In this article we report on properties of these combinatorial objects and on how they reflect properties of the corresponding algebras.