On the FRTS approach to quantized current algebras

1998/04/29 by Jintai Ding, Ding, Jintai, Sergei Khoroshkin +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9804140

AMS-LaTeX, 15pp

arxiv created 1998/07/21 · arxiv updated 2009/11/30

Abstract

We study the possibility to establish L-operator's formalism by Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky (FRST) for quantized current algebras, that is, for quantum affine algebras in the ''new realization '' by V. Drinfeld with the corresponding Hopf algebra structure and for their Yangian counterpart. We establish this formalism using the twisting procedure by Tolstoy and the second author and explain the problems which FRST approach encounter for quantized current algebras. We show also that, for the case of U_q( \frak sl_n), entries of the L-operators of FRTS type give the Drinfeld current operators for the non-simple roots, which we discovered recently. As an application we deduce the commutation relations between these current operators for U_q( \frak sl₃).

Related

• Weyl group extension of quantized current algebras
• Generalized quantum current algebras
• Generalization and Deformation of Drinfeld quantum affine algebras
• Infinite Hopf Families of Algebras and Yang-Baxter Relations
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