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The structures of Hopf $\ast $-algebra on Radford algebras
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 365-377
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We investigate the structures of Hopf $\ast $-algebra on the Radford algebras over $\mathbb {C}$. All the $*$-structures on $H$ are explicitly given. Moreover, these Hopf $*$-algebra structures are classified up to equivalence.
We investigate the structures of Hopf $\ast $-algebra on the Radford algebras over $\mathbb {C}$. All the $*$-structures on $H$ are explicitly given. Moreover, these Hopf $*$-algebra structures are classified up to equivalence.
DOI : 10.21136/CMJ.2018.0319-17
Classification : 16G99, 16T05
Keywords: antilinear map; $\ast $-structure; Hopf $\ast $-algebra 
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Mohammed, Hassan Suleman Esmael; Chen, Hui-Xiang. The structures of Hopf $\ast $-algebra on Radford algebras. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 365-377. doi: 10.21136/CMJ.2018.0319-17

[1] Chen, H. X.: A class of noncommutative and noncocommutative Hopf algebras: The quantum version. Commun. Algebra 27 (1999), 5011-5023. | DOI | MR | JFM

[2] Kassel, C.: Quantum Groups. Graduate Texts in Mathematics 155, Springer, New York (1995). | DOI | MR | JFM

[3] Lorenz, M.: Representations of finite-dimensional Hopf algebras. J. Algebra 188 (1997), 476-505. | DOI | MR | JFM

[4] Majid, S.: Foundations of Quantum Group Theory. Cambridge University Press, Cambridge (1995). | DOI | MR | JFM

[5] Masuda, T., Mimachi, K., Nakagami, Y., Noumi, M., Saburi, Y., Ueno, K.: Unitary representations of the quantum $ SU_q(1,1)$: Structure of the dual space of ${\cal U}_q( sl(2))$. Lett. Math. Phys. 19 (1990), 187-194. | DOI | MR | JFM

[6] Mohammed, H. S. E., Li, T., Chen, H.: Hopf $\ast$-algebra structures on $H(1,q)$. Front. Math. China 10 (2015), 1415-1432. | DOI | MR | JFM

[7] Montgomery, S.: Hopf Algebras and Their Actions on Rings. Regional Conference Series in Mathematics 82, American Mathematical Society, Providence (1993). | DOI | MR | JFM

[8] Podleś, P.: Complex quantum groups and their real representations. Publ. Res. Inst. Math. Sci. 28 (1992), 709-745. | DOI | MR | JFM

[9] Radford, D. E.: The order of the antipode of a finite dimensional Hopf algebra is finite. Am. J. Math. 98 (1976), 333-355. | DOI | MR | JFM

[10] Radford, D. E.: Hopf Algebras. Series on Knots and Everything 49, World Scientific, Hackensack (2012). | DOI | MR | JFM

[11] Sweedler, M. E.: Hopf Algebras. Mathematics Lecture Note Series, W. A. Benjamin, New York (1969). | MR | JFM

[12] Tucker-Simmons, M.: $\ast$-structures on module-algebras. Available at \ifPdf\pdfurl{ | arXiv

[13] Daele, A. Van: The Haar measure on a compact quantum group. Proc. Am. Math. Soc. 123 (1995), 3125-3128. | DOI | MR | JFM

[14] Woronowicz, S. L.: Compact matrix pseudogroups. Commun. Math. Phys. 111 (1987), 613-665. | DOI | MR | JFM

[15] Woronowicz, S. L.: Twisted $ SU(2)$ group. An example of non-commutative differential calculus. Publ. Res. Inst. Math. Sci. 23 (1987), 117-181. | DOI | MR | JFM

[16] Woronowicz, S. L.: Krein-Tannak duality for compact matrix pseudogroups. Twisted $ SU(N)$ groups. Invent. Math. 93 (1988), 35-76. | DOI | MR | JFM

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