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Results tagged with cluster-algebras
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user 750
Questions related to cluster algebras, a class of commutative rings introduced around 2000 by Fomin and Zelevinsky, and nearby topics.
11
votes
1
answer
835
views
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 in …
- 13k
10
votes
1
answer
601
views
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 $\ …
- 13k
8
votes
Are cluster variables prime elements?
Boo. The answer is no. Consider the Markov cluster algebra, whose corresponding matrix is
$$\left[\begin{array}{ccc} 0 & -2 & 2 \\ 2 & 0 & -2 \\ -2 & 2 & 0 \end{array}\right]$$
For an initial clust …
- 13k