On Cluster Variables of Rank Two Acyclic Cluster Algebras

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Preprojective cluster variables of acyclic cluster algebras

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...

متن کامل

Acyclic Quantum Cluster Algebras

This thesis concerns quantum cluster algebras. For skew-symmetric acyclic quantum cluster algebras, we express the quantum F -polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. Then we introduce a new family of graded quiver varieties together with a new t-deformation, and generalize Nakajima’s t-analogue of q-characters to thes...

متن کامل

CLUSTER ALGEBRAS AND CLUSTER CATEGORIES

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...

متن کامل

On the Cluster Multiplication Theorem for Acyclic Cluster Algebras

In [3] and [13], the authors proved the cluster multiplication theorems for finite type and affine type. We generalize their results and prove the cluster multiplication theorem for arbitrary type by using the properties of 2–Calabi–Yau (Auslander–Reiten formula) and high order associativity. Introduction Cluster algebras were introduced by Fomin and Zelevinsky in [9]. By definition, the cluste...

متن کامل

Cluster algebras of infinite rank

Holm and Jørgensen have shown the existence of a cluster structure on a certain category D that shares many properties with finite type A cluster categories and that can be fruitfully considered as an infinite analogue of these. In this work we determine fully the combinatorics of this cluster structure and show that these are the cluster combinatorics of cluster algebras of infinite rank. That...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Annals of Combinatorics

سال: 2012

ISSN: 0218-0006,0219-3094

DOI: 10.1007/s00026-012-0134-9