Piecewise hereditary incidence algebras of Dynkin and extended Dynkin type

Abstract

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 Skowroński. 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.

Keywords:

• Incidence algebra
• piecewise hereditary algebra
• trivial extension

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16D10
• 16G10
• 16G20

Additional information

Funding

Eduardo do N. Marcos was supported by the Thematic Project of FAPESP 2014/09310-5 and also a research grant from CNPq 302003/2018-5. Marcelo Moreira acknowledges support from CAPES, in the form of a PhD Scholarship, PhD made at Programa de Matemática, IME-USP (Brazil).