iecewise hereditary incidence algebras of Dynkin and extended Dynkin typ

Author(s)

Marcos, Eduardo do N. ^[1] ; Moreira, Marcelo ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Alfenas, Inst Ciencias Exatas, Dept Matemat, Alfenas, MG - Brazil

• Document type: Journal article
• Source: COMMUNICATIONS IN ALGEBRA; v. 50, n. 3 SEP 2021.
• Web of Science Citations: 0

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 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. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants