The Coradical Filtration for Drinfeld Double Ringel-Hall Algebras

Abstract

Let 𝒟(Λ) be the Drinfeld double Ringel-Hall algebra with Λ being any finite dimensional hereditary algebra over a finite field k. We determine the coradical filtration for 𝒟(Λ). As an application, we describe the group of Hopf algebra automorphisms of the Drinfeld double Ringel composition algebra of Λ.

Key Words:

• Coradical filtration
• Drinfeld double
• Ringel-Hall algebra
• Hopf automorphism

Mathematics Subject Classification (1991):

• Primary 16W30
• 16G20
• 16G70
• Secondary 16G60
• 05A30
• 16W50
• 16E10
• 17B37
• 18G15

Acknowledgments

The paper was completed during the author's stay in the Mathematics Department of Bielefeld University. He is indebted to Professor C. M. Ringel for his kind hospitality and helpful discussions, and to the Volkswagen Foundation for financial support.

This work is supported in part by the Chinese National Natural Science Foundation and Natural Science Foundation of Jiangsu Province.