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Categorification of Sign-Skew-Symmetric Cluster Algebras and Some Conjectures on g-Vectors

机译:Categorification of Sign-Skew-Symmetric Cluster Algebras and Some Conjectures on g-Vectors

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摘要

Using the unfolding method given in Huang and Li (Adv. Math. 340, 221-283 2018), we prove the conjectures on sign-coherence and a recurrence formula respectively of g-vectors for acyclic sign-skew-symmetric cluster algebras. As a (following) consequence, the conjecture is affirmed in the same case which states that the g-vectors of any cluster form a basis of Z(n). Also, the additive categorification of an acyclic sign-skew-symmetric cluster algebra A(Sigma) is given, which is realized as (C-(Q) over tilde, Gamma)for a Frobenius 2-Calabi-Yau category C-(Q) over tilde constructed from an unfolding (Q, Gamma) of the acyclic exchange matrix B of A(Sigma).

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