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.b160029
Published 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
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