Ringel–Hall Algebras of Quotient Algebras of Path Algebras

Abstract

We determine the generating relations for Ringel–Hall algebras associated with quotient algebras of path algebras of Dynkin and tame quivers, and investigate their connection with composition subalgebras.

Key Words:

• Generating relations
• Path algebras
• Quotient algebras
• Ringel-Hall algebras

2010 Mathematics Subject Classification:

• 17B37
• 16G20

ACKNOWLEDGMENT

The author is grateful to Professor Bangming Deng for his guidance, encouragement and carefully reading the article. We also thank Zhonghua Zhao for many helpful discussions.

This work was supported partially by the Doctoral Program of Higher Education and the Natural Science Foundation of China.

Notes

Communicated by D. Zacharia.