Periodicities in Cluster Algebras and Cluster Automorphism Groups
نویسندگان
چکیده
We study the relations between two groups related to cluster automorphism which are defined by Assem, Schiffler and Shamchenko. establish relationships among (strict) direct those consisting of periodicities labeled seeds exchange matrices, respectively, in language short exact sequences. As an application, we characterize automorphism-finite algebras cases bipartite or finite mutation type. Finally, relation group [Formula: see text] for a algebra class text], give negative answer via counter-examples King Pressland's problem.
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...
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ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2021
ISSN: ['0219-1733', '1005-3867']
DOI: https://doi.org/10.1142/s100538672100047x