Czechoslovak Mathematical Journal

, Volume 69, Issue 2, pp 365–377 | Cite as

The structures of Hopf *-algebra on Radford algebras

  • Hassan Suleman Esmael MohammedEmail author
  • Hui-Xiang ChenEmail author


We investigate the structures of Hopf *-algebra on the Radford algebras over ℂ. All the *-structures on H are explicitly given. Moreover, these Hopf *-algebra structures are classified up to equivalence.


antilinear map *-structure Hopf *-algebra 

MSC 2010

16G99 16T05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. X. Chen: A class of noncommutative and noncocommutative Hopf algebras: The quantum version. Commun. Algebra 27 (1999), 5011–5023.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    C. Kassel: Quantum Groups. Graduate Texts in Mathematics 155, Springer, New York, 1995.CrossRefzbMATHGoogle Scholar
  3. [3]
    M. Lorenz: Representations of finite-dimensional Hopf algebras. J. Algebra 188 (1997), 476–505.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    S. Majid: Foundations of Quantum Group Theory. Cambridge University Press, Cambridge, 1995.CrossRefzbMATHGoogle Scholar
  5. [5]
    T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi, Y. Saburi, K. Ueno: Unitary representations of the quantum SUq(1,1): Structure of the dual space of \({{\cal U}_q}\) (sl(2)). Lett. Math. Phys. 19 (1990), 187–194.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    H. S. E. Mohammed, T. Li, H. Chen: Hopf *-algebra structures on H(1, q). Front. Math. China 10 (2015), 1415–1432.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    S. Montgomery: Hopf Algebras and Their Actions on Rings. Regional Conference Series in Mathematics 82, American Mathematical Society, Providence, 1993.Google Scholar
  8. [8]
    P. Podleś: Complex quantum groups and their real representations. Publ. Res. Inst. Math. Sci. 28 (1992), 709–745.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    D. E. Radford: The order of the antipode of a finite dimensional Hopf algebra is finite. Am. J. Math. 98 (1976), 333–355.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    D. E. Radford: Hopf Algebras. Series on Knots and Everything 49, World Scientific, Hackensack, 2012.zbMATHGoogle Scholar
  11. [11]
    M. E. Sweedler: Hopf Algebras. Mathematics Lecture Note Series, W. A. Benjamin, New York, 1969.zbMATHGoogle Scholar
  12. [12]
    M. Tucker-Simmons: *-structures on module-algebras. Available at
  13. [13]
    A. Van Daele: The Haar measure on a compact quantum group. Proc. Am. Math. Soc. 123 (1995), 3125–3128.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    S. L. Woronowicz: Compact matrix pseudogroups. Commun. Math. Phys. 111 (1987), 613–665.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    S. L. Woronowicz: Twisted SU(2) group. An example of non-commutative differential calculus. Publ. Res. Inst. Math. Sci. 23 (1987), 117–181.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    S. L. Woronowicz: Krein-Tannak duality for compact matrix pseudogroups. Twisted SU(N) groups. Invent. Math. 93 (1988), 35–76.CrossRefzbMATHGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Cz 2019

Authors and Affiliations

  1. 1.School of Mathematical ScienceYangzhou UniversityYangzhouChina

Personalised recommendations