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 Weak Hopf algebras corresponding to non-standard quantum groups Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 463-484 https://doi.org/10.4134/BKMS.b160029Published online March 31, 2017 Cheng Cheng and Shilin Yang Beijing University of Technology, Beijing University of Technology Abstract : We construct a weak Hopf algebra $\wx$ corresponding to non-standard quantum group $X_q(A_1)$. The PBW basis of $\wx$ is described and all the highest weight modules of $\wx$ are classified. Finally we give the Clebsch-Gordan decomposition of the tensor product of two highest weight modules of $\wx$. Keywords : non-standard quantum group, weak Hopf algebra, Clebsch-Gordan decomposition MSC numbers : 16T99, 17B37, 17B10 Downloads: Full-text PDF