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Monoidal categorification and quantum affine algebras.(English)Zbl 1497.17020

Authors’ abstract: We introduce and investigate new invariants of pairs of modules \(M\) and \(N\) over quantum affine algebras \(U'_q (\mathfrak{g})\) by analyzing their associated \(R\)-matrices. Using these new invariants, we provide a criterion for a monoidal category of finite-dimensional integrable \(U'_q (\mathfrak{g})\)-modules to become a monoidal categorification of a cluster algebra.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
13F60 Cluster algebras
18N25 Categorification

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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