科研之友
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摘要
For a skew-symmetrizable cluster algebra A(t0) with principal coefficients at t(0), we prove that each seed Sigma(t) of A(t0) is uniquely determined by its C -matrix, which was proposed by Fomin and Zelevinsky (Compos. Math. 143 (2007), 112{164) as a conjecture. Our proof is based on the fact that the positivity of cluster variables and sign coherence of c-vectors hold for A(t0), which was actually verified in Gross et al. (Canonical bases for cluster algebras, J. Amer. Math. Soc. 31(2) (2018), 497{608). Further discussion is provided in the sign-skew-symmetric case so as to obtain a weak version of the conjecture in this general case.
- 出版日期2020-6
- 单位浙江大学
