Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1019-1028, 2022

Classification of ideals of 8-dimensional Radford Hopf algebra

Yu Wang

Received September 1, 2021. Published online March 31, 2022.

Abstract: Let $H_{m,n}$ be the $mn^2$-dimensional Radford Hopf algebra over an algebraically closed field of characteristic zero. We give the classification of all ideals of $8$-dimensional Radford Hopf algebra $H_{2,2}$ by generators.

Keywords: ideal; Radford Hopf algebra; principal ideal ring

Classification MSC: 16D25, 20G42

DOI: 10.21136/CMJ.2022.0313-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

References:
[1] I. Assem, D. Simson, A. Skowroński: Elements of the Representation Theory of Associative Algebras. Vol. 1. Techniques of Representation Theory. London Mathematical Society Student Texts 65. Cambridge University Press, Cambridge (2006). DOI 10.1017/CBO9780511614309 | MR 2197389 | Zbl 1092.16001
[2] M. Auslander, I. Reiten, S. O. Smalø: Representation Theory of Artin Algebras. Cambridge Studies in Advanced Mathematics 36. Cambridge University Press, Cambridge (1995). DOI 10.1017/CBO9780511623608 | MR 1314422 | Zbl 0834.16001
[3] C. Kassel: Quantum Groups. Graduate Texts in Mathematics 155. Springer, New York (1995). DOI 10.1007/978-1-4612-0783-2 | MR 1321145 | Zbl 0808.17003
[4] S. Montgomery: Hopf Algebras and Their Actions on Rings. Regional Conference Series in Mathematics 82. American Mathematical Society, Providence (1993). DOI 10.1090/cbms/082 | MR 1243637 | Zbl 0793.16029
[5] D. E. Radford: On the coradical of a finite-dimensional Hopf algebra. Proc. Am. Math. Soc. 53 (1975), 9-15. DOI 10.1090/S0002-9939-1975-0396652-0 | MR 396652 | Zbl 0324.16009
[6] Z. Wang, L. Li, Y. Zhang: Green rings of pointed rank one Hopf algebras of nilpotent type. Algebr. Represent. Theory 17 (2014), 1901-1924. DOI 10.1007/s10468-014-9484-9 | MR 3284336 | Zbl 1318.16032
[7] Z. Wang, L. Li, Y. Zhang: Green rings of pointed rank one Hopf algebras of non-nilpotent type. J. Algebra 449 (2016), 108-137. DOI 10.1016/j.jalgebra.2015.11.002 | MR 3448167 | Zbl 1338.16039
[8] Y. Wang, Y. Zheng, L. Li: On the ideals of the Radford Hopf algebras. Commun. Algebra 49 (2021), 4109-4122. DOI 10.1080/00927872.2021.1914073 | MR 4296825 | Zbl 07431245

Affiliations: Yu Wang, School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, Jiangsu 213001, P. R. China, e-mail: yu.wang@mail.sdu.edu.cn

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