# WEAK HOPF ALGEBRAS CORRESPONDING TO NON-STANDARD QUANTUM GROUPS

• Cheng, Cheng (College of Applied Sciences Beijing University of Technology) ;
• Yang, Shilin (College of Applied Sciences Beijing University of Technology)
• Published : 2017.03.31

#### Abstract

We construct a weak Hopf algebra $wX_q(A_1)$ corresponding to non-standard quantum group $X_q(A_1)$. The PBW basis of $wX_q(A_1)$ is described and all the highest weight modules of $wX_q(A_1)$ are classified. Finally we give the Clebsch-Gordan decomposition of the tensor product of two highest weight modules of $wX_q(A_1)$.

#### Acknowledgement

Supported by : National Natural Science Foundation of China, Beijing Natural Science Foundation

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#### Cited by

1. PBW Basis of Non-standard Quantum Groups Xq(An) vol.7, pp.3, 2017, https://doi.org/10.17706/ijapm.2017.7.3.191-199