The Double Ringel-Hall Algebras of Valued Quivers*

Abstract

This paper is devoted to the study of the structure of the double Ringel-Hall algebra ${\user1{\mathcal{D}}}{\left( \Lambda \right)}$ for an infinite dimensional hereditary algebra Λ, which is given by a valued quiver Γ over a finite field, and also to the study of the relations of ${\user1{\mathcal{D}}}{\left( \Lambda \right)}$-modules with representations of valued quiver Γ.

Keywords

Ringel-Hall algebras / Generalized Kac-Moody algebras / Drinfeld double / 16G10 / 17B37 / 17B67

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