کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4583915 | 1630456 | 2016 | 35 صفحه PDF | دانلود رایگان |

We study rooted cluster algebras and rooted cluster morphisms which were introduced in [1] recently and cluster structures in 2-Calabi–Yau triangulated categories. An example of rooted cluster morphism which is not ideal is given, this clarifying a doubt in [1]. We introduce the notion of freezing of a seed and show that an injective rooted cluster morphism always arises from a freezing and a subseed. Moreover, it is a section if and only if it arises from a subseed. This answers the Problem 7.7 in [1]. We prove that an inducible rooted cluster morphism is ideal if and only if it can be decomposed as a surjective rooted cluster morphism and an injective rooted cluster morphism. For rooted cluster algebras arising from a 2-Calabi–Yau triangulated category CC with cluster tilting objects, we give an one-to-one correspondence between certain pairs of their rooted cluster subalgebras which we call complete pairs (see Definition 2.27) and cotorsion pairs in CC.
Journal: Journal of Algebra - Volume 458, 15 July 2016, Pages 387–421