Questions tagged [cluster-algebras]
Questions related to cluster algebras, a class of commutative rings introduced around 2000 by Fomin and Zelevinsky, and nearby topics.
104 questions
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Do Denominator Vectors Determine the Cluster Variable
Given a cluster algebra $A=A(\mathbf{x},Q)$, the Laurent Phenomenon states that all the cluster variables of $A$ are Laurent polynomials in the elements of $\mathbf{x}$. Thus, any cluster variable $y$...
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Are cluster variables prime elements?
Cluster algebras introduction
A cluster algebra is a subalgebra $A$ of $k[x_1^{\pm1},...,x_n^{\pm1}]$ generated by a set of cluster variables, which are elements which can be generated from the set $\{...
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Which cluster algebras have been categorified?
In "Tilting Theory and Cluster Combinatorics" Buan, Marsh, Reineke, Reiten, and Todorov constructed cluster categories for mutation finite cluster algebras (without coefficients), and Amiot gives a ...
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11
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Which cluster algebras are coordinate rings of double Bruhat cells?
Background
A uselessly vague paragraph follows. A cluster algebra is a commutative algebra $A$ with a distinguished set of generators called cluster variables. These cluster variables are grouped ...
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