Abstract: |
Cluster algebras are commutative algebras introduced by Fomin and Zelevinsky, which are generated by some distinguished elements called the cluster variables. These algebras are applied to Poisson geometry, representation theory of associative algebras, string theory, and so on. The cluster variables are given by applying the mutations repeatedly starting from the initial cluster variables. Thanks to the separation formulas, the cluster variables, and the coefficients are described by the C-matrices, the G-matrices, and the F-polynomials. These matrices and polynomials are studied to know the properties of the cluster variables or mutations. In particular, I consider the F-matrices, which are the “degree matrices” of the F-polynomials, and these column vectors, the f-vectors. In this talk, I will introduce them and these properties. |