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Results tagged with cluster-algebras
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user 10881
Questions related to cluster algebras, a class of commutative rings introduced around 2000 by Fomin and Zelevinsky, and nearby topics.
1
vote
About cluster variables obtained by (sequentially) mutating at exchangeable variables from a...
Not really an answer, but a comment about the related question:
Can one reach every cluster in that way ?
It is rather easy to check (using sagemath or Keller's applet) that for the cyclic quiver in …
- 3,597
3
votes
Grassmannian cluster algebra of infinite type has no trees in its mutation class
Regarding question Q2, one can go a little bit further and describe simple diagrams with few edges for some more cases.
Let us talk about $Gr(p, p+q)$, so that there is a symmetry between $p$ and $q$. …
- 3,597
2
votes
Accepted
Number of cluster variables
For $A_k$ of level $\ell$, the cluster types are given by square grids of size $k \times \ell$.
Therefore the types you ask for are $E_6$ and $E_8$ (see Scott - Grassmannians and cluster algebras), fo …
- 3,597
2
votes
Kahler differentials on cluster varieties
There is not much known in general, as far as I know.
There is a nice 2-form (called the Weil-Petersson 2-form) defined using the cluster algebra structure.
This can be found in article "The Weil-Pe …
- 3,597
6
votes
0
answers
339
views
cluster variables and L-functions
There is something in common between
cluster variables in the theory of cluster algebras,
L-functions in number theory,
namely the fact that both map direct sums to products, just like determinant …
- 3,597