Tame concealed algebras and cluster quivers of minimal infinite type
نویسندگان
چکیده
منابع مشابه
Integral Bases of Cluster Algebras and Representations of Tame Quivers
In [CK] and [SZ], the authors constructed the bases of cluster algebras of finite types and of type e A1,1, respectively. In this paper, we will deduce Z-bases for cluster algebras of affine types and compare Z-bases with generic variables in [Du2]. Moreover, we give inductive formulas for computing the multiplication between two generalized cluster variables associated to objects in a tube.
متن کاملTame Quivers and Affine Enveloping Algebras
Let g be an affine Kac-Moody algebra with symmetric Cartan datum, n be the maximal nilpotent subalgebra of g. By the Hall algebra approach, we construct integral bases of the Z-form of the enveloping algebra U(n). In particular, the representation theory of tame quivers is essentially used in this paper.
متن کاملCluster 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 کاملMutation classes of Ãn−quivers and derived equivalence classification of cluster tilted algebras of type Ãn
We give an explicit description of the mutation classes of quivers of type Ãn. Furthermore, we provide a complete classification of cluster tilted algebras of type Ãn up to derived equivalence. We show that the bounded derived category of such an algebra depends on four combinatorial parameters of the corresponding quiver.
متن کاملCLUSTER 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 کاملذخیره 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: Journal of Pure and Applied Algebra
سال: 2007
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2006.12.007