3
votes
2answers
205 views

Kahler differentials on cluster varieties

On affine toric varieties there is a classical theorem of Danilov which gives some combinatorial ways to describe the global sections of an appropriate sheaf of Kahler differentials as a vector space. ...
5
votes
0answers
125 views

Non-crystallographic cluster algebras

Background Fomin and Zelevinsky have introduced cluster algebras in an influential article. To define a cluster algebra, Fomin and Zelevinsky have defined a mutation of seeds. Here, a seed ...
8
votes
1answer
406 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 ...
9
votes
1answer
370 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 ...