Structure of seeds in generalized cluster algebras

Abstract

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.

15 pages; v2:minor revision; v3:typos corrected, to appear in Pacific J. Math

References in corpus (2)

• Exact WKB analysis and cluster algebras II: Simple poles, orbifold points, and generalized cluster algebras
• Quantum affine algebras at roots of unity and generalised cluster algebras

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