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Two-parameter quantum affine algebra \(U_{r,s}(\widehat{\mathfrak {sl}_n})\), Drinfel’d realization and quantum affine Lyndon basis.(English)Zbl 1236.17021

Summary: We further define two-parameter quantum affine algebra \(U_{r,s}(\widehat{\mathfrak {sl}_n})(n > 2)\) after the work on the finite cases, which turns out to be a Drinfel’d double. Of importance for the quantum affine cases is that we can work out the compatible two-parameter version of the Drinfel’d realization as a quantum affinization of \(U_{r,s}({\mathfrak{sl}}_n)\) and establish the Drinfel’d Isomorphism Theorem in the two-parameter setting, via developing a new combinatorial approach (quantum calculation) to the quantum affine Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel’d generators).

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory

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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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