منابع مشابه
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 کاملGraded Quantum Cluster Algebras of Infinite Rank as Colimits
We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of infinite rank can be written as a colimit of graded quantum cluster algebras of finite rank. As an application, for each k we construct a graded quantum infinite Grassmannian admitting a cluster algebra structure, exte...
متن کامل- Algebras of Infinite Real Rank
We introduce the notion of weakly (strongly) infinite real rank for unital C∗-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C(X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C∗-algebra C∗ (F∞) of the free group on countable number of generators ha...
متن کاملOn the Loewy Rank of Infinite Algebras
The Loewy rank of a complete lattice L is deened as follows. Take the meet a 1 of all coatoms of L. Then let a 2 be the meet of all lower covers of a 1. Iterate this process to deene a for every ordinal by letting a +1 be the meet of all lower covers of a , and a the meet of all a (for <) if is a limit ordinal. The Loewy rank of L is the smallest ordinal for which a is the zero of L, and the sy...
متن کاملAutomorphisms of Cluster Algebras of Rank 2
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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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2013
ISSN: 0024-6107
DOI: 10.1112/jlms/jdt064