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The Double Ringel-Hall Algebras of Valued Quivers*

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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.

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Correspondence to Yanxin Wang.

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* Project supported by the National Natural Science Foundation of China (No.10471071) and the 973 Project of the Ministry of Science and Technology of China.

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Wang, Y., Xiao, J. The Double Ringel-Hall Algebras of Valued Quivers*. Chin. Ann. Math. Ser. B 27, 701–722 (2006). https://doi.org/10.1007/s11401-005-0287-5

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