CLUSTER AUTOMORPHISMS AND COMPATIBILITY OF CLUSTER VARIABLES
نویسندگان
چکیده
منابع مشابه
Cluster automorphisms and compatibility of cluster variables
In this paper, we introduce a notion of unistructural cluster algebras, for which the set of cluster variables uniquely determines the clusters. We prove that cluster algebras of Dynkin type and cluster algebras of rank 2 are unistructural, then prove that if A is unistructural or of Euclidean type, then f : A → A is a cluster automorphism if and only if f is an automorphism of the ambient fiel...
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These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...
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It is proved that any cluster-tilted algebra defined in the cluster category C(H) has the same representation type as the initial hereditary algebra H . For any valued quiver (Γ,Ω), an injection from the subset PI(Ω) of the cluster category C(Ω) consisting of indecomposable preprojective objects, preinjective objects and the first shifts of indecomposable projective modules to the set of cluste...
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We compute the automorphism group of the affine surfaces with the coordinate ring isomorphic to a cluster algebra of rank 2.
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these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2014
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089514000214