Abstract
We introduce and investigate new invariants of pairs of modules$M$and$N$over quantum affine algebras$U_{q}^{\prime }(\mathfrak{g})$by analyzing their associated$R$-matrices. Using these new invariants, we provide a criterion for a monoidal category of finite-dimensional integrable$U_{q}^{\prime }(\mathfrak{g})$-modules to become a monoidal categorification of a cluster algebra.
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