JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 40-45.doi: 10.6040/j.issn.1671-9352.0.2023.390

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The Hopf algebraic automorphism group of quantum double of 8-dimensional Radford Hopf algebra

HU Mi, SUN Hua*, LI Libin   

  1. School of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Published:2024-12-12

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Abstract: Let R2,2(-1) be the 8-dimensional Radford Hopf algebra, and D(R2,2(-1)) the quantum double of R2,2(-1), it is proved that the Hopf algebraic automorphism group of D(R2,2(-1)) is isomorphic to Klein four-group.

Key words: Hopf algebra, quantum double, automorphism group

CLC Number: 

  • O153.3
[1] DRINFELD V G. Hopf algebra and the Yang-Baxter equation[J]. Soviet Math Dokl, 1985, 32(1):254-258.
[2] RADFORD D E. On the coradical of a finite-dimensional Hopf algebra[J]. Proceedings of the American Mat-hematical Society, 1975, 53(1):9-15.
[3] KROP L, RADFORD D E. Finite-dimensional Hopf algebras of rank one in characteristic zero[J]. Journal of Algebra, 2006, 302:214-230.
[4] SUN Hua, CHEN Huixiang. Representations of Drinfeld doubles of Radford Hopf algebras[EB/OL].(2023-04-17)[2023-11-17]. https://arxiv.org/abs/2304.04908.
[5] WANG Zhihua, LI Libin, ZANG Yinhuo. Green rings of pointed rank one Hopf algebras of non-nilpotent type[J]. Journal of Algebra, 2016, 449:108-137.
[6] SWEEDLER M E. Hopf algebras[M]. New York: Benjamin, 1969:49-90.
[7] KASSEL C. Quantum groups[M]. New York: Springer, 1995:39-56.
[8] MONTGOMERY S. Hopf algebras and their actions on rings[M]. Island: Amer Math Soc, 1993:1-9.
[9] 杜娜. Hopf代数的拟三角结构及其自同构群[D]. 北京:北京工业大学, 2020. DU Na. The quasitriangular structures and the group of automorphisms of Hopf algebras[D]. Beijing: Beijing University of Technology, 2020.
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