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Bull. Korean Math. Soc. 2017; 54(2): 463-484

Online first article March 13, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b160029

Copyright © The Korean Mathematical Society.

Weak Hopf algebras corresponding to non-standard quantum groups

Cheng Cheng and Shilin Yang

Beijing University of Technology, Beijing University of Technology

Abstract

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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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