Exceptional Components

Abstract

For a wild acyclic quiver Q, Kerner introduced the notion of exceptional components for the Auslander–Reiten quiver of Q over an algebraically closed field k. He then defined two invariants for these exceptional components and asked whether these invariants coincide for each exceptional component. He showed that for each exceptional component there is a related hereditary factor algebra B of the path algebra kQ. He then proved that B is tame or representation finite and asked whether the representation finite case does occur, at all. We will answer both of Kerner's questions.

Key Words:

• Regular component
• Wild hereditary algebra

2000 Mathematics Subject Classification:

• Primary 16G20
• Secondary 16G60

Notes

Communicated by D. Zacharia.