Abstract
Let H be a hereditary algebra of Dynkin type D n over a field k and 𝒞 H be the cluster category of H. Assume that n ≥ 5 and that T and T′ are tilting objects in 𝒞 H . We prove that the cluster-tilted algebra Γ = End𝒞 H (T)op is isomorphic to Γ′ = End𝒞 H (T′)op if and only if T = τ i T′ or T = στ j T′ for some integers i and j, where τ is the Auslander–Reiten translation and σ is the automorphism of 𝒞 H defined in Section 4.
ACKNOWLEDGMENTS
After completing this work, the third author was informed by Aslak Buan and Hermund Torkildsen that they also proved the parallel results with this article in [Citation6]; he is grateful to them for this.
Supported by the NSF of China (Grant No. 10771112) and of the NSF of Shandong province (Grant No. Y2008A05)
Dedicated to Professor Shaoxue Liu on the occasion of his 80th birthday.
Notes
Communicated by Q. Wu.