Master Degree Project Presentation: Classification of quivers over truncated polynomial rings

Abstract: Gabriel's theorem classifies quivers over an arbitrary field and characterizes quivers of finite representation type using Dynkin diagrams. We extend this theorem by replacing the ground fields with truncated polynomial rings through covering theory and the knitting algorithm. Furthermore, we classify the monomorphism category of quivers over truncated polynomial rings and establish a connection with Gabriel's theorem.