Piecewise hereditary incidence algebras of Dynkin and extended Dynkin type

摘要

Let K Delta be the incidence algebra of a poset . We study some aspects of incidence algebras K Delta that are piecewise hereditary, which we denominate PHI algebras. We describe the quiver with relations of the PHI algebras of Dynkin type. Also we introduce a new family of PHI algebras of extended Dynkin type, which we call ANS family, in reference to Assem, Nehring, and Skowronski. In this description, the important method was the one of cutting sets on trivial extensions. We implemented this method in the computer algebra system GAP/QPA to shows exactly the quivers with relations resulted.