The structures of Hopf * -algebra on Radford algebras

Hassan Suleman Esmael Mohammed; Hui-Xiang Chen

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 2, page 365-377
  • ISSN: 0011-4642

Abstract

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

How to cite

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Mohammed, Hassan Suleman Esmael, and Chen, Hui-Xiang. "The structures of Hopf $\ast $-algebra on Radford algebras." Czechoslovak Mathematical Journal 69.2 (2019): 365-377. <http://eudml.org/doc/294397>.

@article{Mohammed2019,
abstract = {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.},
author = {Mohammed, Hassan Suleman Esmael, Chen, Hui-Xiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {antilinear map; $\ast $-structure; Hopf $\ast $-algebra},
language = {eng},
number = {2},
pages = {365-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The structures of Hopf $\ast $-algebra on Radford algebras},
url = {http://eudml.org/doc/294397},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Mohammed, Hassan Suleman Esmael
AU - Chen, Hui-Xiang
TI - The structures of Hopf $\ast $-algebra on Radford algebras
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 365
EP - 377
AB - 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.
LA - eng
KW - antilinear map; $\ast $-structure; Hopf $\ast $-algebra
UR - http://eudml.org/doc/294397
ER -

References

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  1. Chen, H. X., 10.1080/00927879908826745, Commun. Algebra 27 (1999), 5011-5023. (1999) Zbl0942.16038MR1709261DOI10.1080/00927879908826745
  2. Kassel, C., 10.1007/978-1-4612-0783-2, Graduate Texts in Mathematics 155, Springer, New York (1995). (1995) Zbl0808.17003MR1321145DOI10.1007/978-1-4612-0783-2
  3. Lorenz, M., 10.1006/jabr.1996.6827, J. Algebra 188 (1997), 476-505. (1997) Zbl0873.16023MR1435369DOI10.1006/jabr.1996.6827
  4. Majid, S., 10.1017/CBO9780511613104, Cambridge University Press, Cambridge (1995). (1995) Zbl0857.17009MR1381692DOI10.1017/CBO9780511613104
  5. Masuda, T., Mimachi, K., Nakagami, Y., Noumi, M., Saburi, Y., Ueno, K., 10.1007/BF01039311, Lett. Math. Phys. 19 (1990), 187-194. (1990) Zbl0704.17007MR1046342DOI10.1007/BF01039311
  6. Mohammed, H. S. E., Li, T., Chen, H., 10.1007/s11464-015-0454-2, Front. Math. China 10 (2015), 1415-1432. (2015) Zbl1341.16035MR3403203DOI10.1007/s11464-015-0454-2
  7. Montgomery, S., 10.1090/cbms/082, Regional Conference Series in Mathematics 82, American Mathematical Society, Providence (1993). (1993) Zbl0793.16029MR1243637DOI10.1090/cbms/082
  8. Podleś, P., 10.2977/prims/1195167933, Publ. Res. Inst. Math. Sci. 28 (1992), 709-745. (1992) Zbl0809.17003MR1195996DOI10.2977/prims/1195167933
  9. Radford, D. E., 10.2307/2373888, Am. J. Math. 98 (1976), 333-355. (1976) Zbl0332.16007MR0407069DOI10.2307/2373888
  10. Radford, D. E., 10.1142/9789814338660, Series on Knots and Everything 49, World Scientific, Hackensack (2012). (2012) Zbl1266.16036MR2894855DOI10.1142/9789814338660
  11. Sweedler, M. E., Hopf Algebras, Mathematics Lecture Note Series, W. A. Benjamin, New York (1969). (1969) Zbl0194.32901MR0252485
  12. Tucker-Simmons, M., * -structures on module-algebras, Available at https://arxiv.org/abs/1211.6652v2https://arxiv.org/https://arxiv.org/abs/1211.6652v2abs/1211.6652v2. 
  13. Daele, A. Van, 10.2307/2160670, Proc. Am. Math. Soc. 123 (1995), 3125-3128. (1995) Zbl0844.46032MR1277138DOI10.2307/2160670
  14. Woronowicz, S. L., 10.1007/BF01219077, Commun. Math. Phys. 111 (1987), 613-665. (1987) Zbl0627.58034MR0901157DOI10.1007/BF01219077
  15. Woronowicz, S. L., 10.2977/prims/1195176848, Publ. Res. Inst. Math. Sci. 23 (1987), 117-181. (1987) Zbl0676.46050MR0890482DOI10.2977/prims/1195176848
  16. Woronowicz, S. L., 10.1007/BF01393687, Invent. Math. 93 (1988), 35-76. (1988) Zbl0664.58044MR0943923DOI10.1007/BF01393687

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