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Research Articles

On Hopf algebras whose coradical is a cocentral abelian cleft extension

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Pages 3209-3236 | Received 20 Jul 2023, Accepted 29 Jan 2024, Published online: 21 Feb 2024

References

  • Andruskiewitsch, N. (2017). An introduction to Nichols algebras. In: Cardona, A., Morales, P., Ocampo, H., Paycha, S., Reyes, A., eds. Quantization, Geometry and Noncommutative Structures in Mathematics and Physics. Mathematical Physics Studies. Cham: Springer, pp. 135–195.
  • Andruskiewitsch, N., Angiono, I. (2020). On Nichols algebras over basic Hopf algebras. Math. Z. 296(3–4):1429–1469. DOI: 10.1007/s00209-020-02493-w.
  • Andruskiewitsch, N., Angiono, I., Heckenberger, I. (2020). On Nichols algebras of infinite rank with finite Gelfand-Kirillov dimension. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31(1):81–101.
  • Andruskiewitsch, N., Cuadra, J. (2013). On the structure of (co-Frobenius) Hopf algebras. J. Noncommut. Geom. 7(1):83–104. DOI: 10.4171/jncg/109.
  • Andruskiewitsch, N., Schneider, H-J. (2010). On the classification of finite-dimensional pointed Hopf algebras. Ann. Math. (2) 171(1):375–417. DOI: 10.4007/annals.2010.171.375.
  • Andruskiewitsch, N., Fantino, F. (2007). On pointed Hopf algebras associated with alternating and dihedral groups. Rev. Union Mat. Argent. 48:57–71.
  • Andruskiewitsch, N., Fantino, F., García, G. A., Vendramin, L. (2011). On Nichols algebras associated to simple racks. Contemp. Math. 537:31–56.
  • Andruskiewitsch, N., Galindo, C., Müller, M. (2017). Examples of finite-dimensional Hopf algebras with the dual Chevalley property. Publ. Mat. 61(2):445–474. DOI: 10.5565/PUBLMAT6121705.
  • Andruskiewitsch, N., Graña, M. (2003). From racks to pointed Hopf algebras. Adv. Math. 178(2):177–243. DOI: 10.1016/S0001-8708(02)00071-3.
  • Andruskiewitsch, N., Heckenberger, I., Schneider, H.-J. (2010). The Nichols algebra of a semisimple Yetter-Drinfeld module. Amer. J. Math. 132(6):1493–1547. DOI: 10.1353/ajm.2010.a404140.
  • Andruskiewitsch, N., Vay, C. (2011). Finite dimensional Hopf algebras over the dual group algebra of the symmetric group in three letters. Commun. Algebra 39(12):4507–4517. DOI: 10.1080/00927872.2011.616429.
  • Angiono, I. (2015). A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems. J. Eur. Math. Soc. 17:2643–2671. DOI: 10.4171/jems/567.
  • Bagio, D,; García, G. A., Giraldi, J. M. J., Márquez, O. (2021). Finite-dimensional Nichols algebras over dual Radford algebras. J. Algebra Appl. 20(1):Paper No. 2140001, 39 pp. DOI: 10.1142/S0219498821400016.
  • Fantino, F., García, G. A. (2011). On pointed Hopf algebras over dihedral groups. Pacific J. Math. 252(1):69–91. DOI: 10.2140/pjm.2011.252.69.
  • García, G. A., García Iglesias, A. (2011). Finite dimensional pointed Hopf algebras over S4 . Israel J. Math. 183:417–444.
  • García, G. A., Giraldi, J. M. J. (2019). On Hopf algebras over quantum subgroups. J. Pure Appl. Algebra 223:738–768. DOI: 10.1016/j.jpaa.2018.04.018.
  • García Iglesias, A., Vay, C. (2014). Finite-dimensional pointed or copointed Hopf algebras over affine racks. J. Algebra 397:379–406. DOI: 10.1016/j.jalgebra.2013.09.009.
  • Graña, M. (2000). On Nichols algebras of low dimension. In: New Trends in Hopf Algebra Theory (La Falda, 1999). Contemporary Mathematics, 267. Providence, RI: American Mathematical Society, pp. 111–134.
  • Heckenberger, I. (2009). Classification of arithmetic root systems. Adv. Math. 220(1):59–124. DOI: 10.1016/j.aim.2008.08.005.
  • Heckenberger, I., Mehir, E., Vendramin, L. Simple Yetter-Drinfeld modules over groups with prime dimension and a finite-dimensional Nichols algebra. https://arxiv.org/abs/2306.02989.
  • Heckenberger, I., Schneider, H.-J. (2020). Hopf Algebras and Root Systems. Mathematical Surveys and Monographs, 247. Providence, RI: American Mathematical Society, xix + 582 pp.
  • Kac, G. I. (1968). Extensions of groups to ring groups. Mat. Sb. 5:451–474. DOI: 10.1070/SM1968v005n03ABEH003627.
  • Mastnak, M. (2002). Hopf algebra extensions arising from semi-direct product of groups. J. Algebra 251:413–434. DOI: 10.1006/jabr.2002.9145.
  • Masuoka, A. (1997). Calculations of some groups of Hopf algebra extensions. J. Algebra 191:568–588. DOI: 10.1006/jabr.1996.6863.
  • Nichols, W. D., Zoeller, M. B. (1989). A Hopf algebra freeness theorem. Amer. J. Math. 111(2):381–385. DOI: 10.2307/2374514.
  • Radford, D. E. (2012). Hopf Algebras. Series on Knots and Everything, Vol. 49. Hackensack, NJ: World Scientific Publishing Co. Pte. Ltd.
  • Radford, D. E. (2003). On oriented quantum algebras derived from representations of the quantum double of a finite-dimensional Hopf algebra. J. Algebra 270(2):670–695. DOI: 10.1016/j.jalgebra.2003.07.006.
  • Serre, J. P. (1977). Linear Representations of Finite Groups. Translated from the second French edition by Leonard L. Scott. Graduate Texts in Mathematics, Vol. 42. New York-Heidelberg: Springer-Verlag, x+170 pp.
  • Shi, Y. (2019). Finite-dimensional Hopf algebras over the Kac-Paljutkin algebra H8. Rev. Un. Mat. Argentina 60(1):265–298. DOI: 10.33044/revuma.v60n1a17.
  • Vendramin, L. (2012). Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent. Proc. Amer. Math. Soc. 140(11):3715–3723. DOI: 10.1090/S0002-9939-2012-11215-8.
  • Xiong, R. (2019). On Hopf algebras over the unique 12-dimensional Hopf algebra without the dual Chevalley property. Commun. Algebra 47(4):1516–1540. DOI: 10.1080/00927872.2018.1508582.
  • Xiong, R., Hu, N. (2022). Classification of finite-dimensional Hopf algebras over dual Radford algebras. Bull. Belg. Math. Soc. Simon Stevin 28(5):633–688. DOI: 10.36045/j.bbms.210612.
  • Zheng, Y., Gao, Y., Hu, N., Shi, Y. (2023). On some classification of finite-dimensional Hopf algebras over the Hopf algebra Hb1* Kashina. Commun. Algebra 51(1):350–371.
  • Zheng, Y., Gao, Y., Hu, N. (2021). Finite-dimensional Hopf algebras over the Hopf algebra Hb:1 of Kashina. J. Algebra 567:613–659.
  • Zheng, Y., Gao, Y., Hu, N. (2021). Finite-dimensional Hopf algebras over the Hopf algebra Hd:−1,1 of Kashina. J. Pure Appl. Algebra 225(4):Paper No. 106527, 37 pp.
  • Zhu, Y. (1994). Hopf algebras of prime dimension. Int. Math. Res. Not. 1: 53–59.

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