Cluster automorphism groups of cluster algebras of finite type
نویسندگان
چکیده
منابع مشابه
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 کاملCluster-tilted Algebras of Finite Representation Type
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a (basic) cluster-tilted algebra of finite type is uniquely determined by its quiver. Also some necessary conditions on the shapes of quivers of cluster-tilted a...
متن کاملRecognizing Cluster Algebras of Finite Type
Cluster algebras were introduced in [5] by Fomin and Zelevinsky to provide an algebraic framework for the study of canonical bases in quantum groups. Since their introduction, it has also been observed that cluster algebras are closely related with different areas in mathematics. For example; they provide a natural algebraic setup to study recursively defined rational functions in combinatorics...
متن کاملOn quantum cluster algebras of finite type
We extend the definition of a quantum analogue of the CalderoChapoton map defined [17]. When Q is a quiver of finite type, we prove that the algebra A H |k|(Q) generated by all cluster characters (see Definition 1) is exactly the quantum cluster algebra E H |k|(Q).
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 generators of ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.09.045