Structure of seeds in generalized cluster algebras

Tomoki Nakanishi
2015 Pacific Journal of Mathematics  
We study generalized cluster algebras introduced by Chekhov and Shapiro. When the coefficients satisfy the normalization and quasi-reciprocity conditions, one can naturally extend the structure theory of seeds in the ordinary cluster algebras by Fomin and Zelevinsky to generalized cluster algebras. As the main result, we obtain formulas expressing cluster variables and coefficients in terms of c-vectors, g-vectors, and F-polynomials.
doi:10.2140/pjm.2015.277.201 fatcat:32lrjaux4befdhtz2jyqjecpyq