Pre-Projective Parts of Tilting Quivers Over Certain Path Algebras

Abstract

Happel and Unger defined a partial order on the set of basic tilting modules. We study the poset of basic preprojective tilting modules over path algebras of representation-infinite type. First we will give a criterion for Ext-vanishing for preprojective modules. With the using of this result, we will give combinatorial characterizations of the poset of basic preprojective tilting modules. Finally, we will see the structure of a preprojective part of tilting quivers.

Key Words:

• Representations of quivers
• Tilting modules

2010 Mathematics Subject Classification:

• Primary 16G20
• Secondary 16D80

ACKNOWLEDGMENT

The author would like to express his gratitude to Professor Susumu Ariki for his mathematical supports and warm encouragements.

Notes

Communicated by D. ladrania.