Cluster-Tilted Algebras of Type D n |
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Authors: | Wenxu Ge Hongbo Lv |
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Affiliation: | School of Mathematics , Shandong University , Jinan, China |
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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. |
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Keywords: | Cluster category Cluster-tilted algebra Cluster tilting object Punctured polygon Triangulation |
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