کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4584014 1630467 2016 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Cluster automorphism groups of cluster algebras of finite type
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Cluster automorphism groups of cluster algebras of finite type
چکیده انگلیسی

We study the cluster automorphism group Aut(A)Aut(A) of a coefficient free cluster algebra AA of finite type. A cluster automorphism of AA is a permutation of the cluster variable set XX that is compatible with cluster mutations. We show that, on the one hand, by the well-known correspondence between XX and the almost positive root system Φ≥−1Φ≥−1 of the corresponding Dynkin type, the piecewise-linear transformations τ+τ+ and τ−τ− on Φ≥−1Φ≥−1 induce cluster automorphisms f+f+ and f−f− of AA respectively; on the other hand, excepting type D2nD2n (n⩾2n⩾2), all the cluster automorphisms of AA are compositions of f+f+ and f−f−. For a cluster algebra of type D2nD2n (n⩾2n⩾2), there exists an exceptional cluster automorphism induced by a permutation of negative simple roots in Φ≥−1Φ≥−1, which is not a composition of τ+τ+ and τ−τ−. By using these results and folding a simply laced cluster algebra, we compute the cluster automorphism group for a non-simply laced finite type cluster algebra. As an application, we show that Aut(A)Aut(A) is isomorphic to the cluster automorphism group of the FZ  -universal cluster algebra of AA.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 447, 1 February 2016, Pages 490–515
نویسندگان
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