Abstract
Buan, Marsh, and Reiten proved that if a cluster-tilting object T in a cluster category 𝒞 associated to an acyclic quiver Q satisfies certain conditions with respect to the exchange pairs in 𝒞, then the denominator in its reduced form of every cluster variable in the cluster algebra associated to Q has exponents given by the dimension vector of the corresponding module over the endomorphism algebra of T. In this article, we give an alternative proof of this result using the Caldero–Keller approach to acyclic cluster algebras and the work of Palu on cluster characters.
ACKNOWLEDGMENTS
The author would like to thank Idun Reiten for corrections and interesting remarks concerning the subject. He would also like to thank the coordinators of the Liegrits network for organizing his stay at the NTNU in Trondheim where this article was written.
Notes
Communicated by C. Cibils.