• Title, Summary, Keyword: weak Hopf algebra

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Department of Mathematics, Dongeui University

  • Yoon, Suk-Bong
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.527-541
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    • 2001
  • We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with th dual cocycle $\alpha$ to afford a Hopf algebra (A equation,※See Full-text). If B and H are finite algebra and Hopf algebra, respectively, then the linear dual (※See Full-text) is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras (※See Full-text).

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WEAK HOPF ALGEBRAS CORRESPONDING TO NON-STANDARD QUANTUM GROUPS

  • Cheng, Cheng;Yang, Shilin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.463-484
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    • 2017
  • 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 $wX_q(A_1)$.