On Homomorphisms from Ringel-hall Algebras to Quantum Cluster Algebras
نویسندگان
چکیده
In [1],the authors defined algebra homomorphisms from the dual RingelHall algebra of certain hereditary abelian categoryA to an appropriate q-polynomial algebra. In the case that A is the representation category of an acyclic quiver, we give an alternative proof by using the cluster multiplication formulas in [9]. Moreover, if the underlying graph of Q is bipartite and the matrix B associated to the quiver Q is of full rank, we show that the image of the algebra homomorphisms is in the corresponding quantum cluster algebra.
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