The Grothendieck ring of Yetter-Drinfeld modules over a class of 2n²-dimensional Kac-Paljutkin Hopf algebras

References

• Andruskiewitsch, N., Schneider, H.-J. (1998). Lifting of quantum linear spaces and pointed Hopf algebras of order p3. J. Algebra 209(2):658–691. DOI: 10.1006/jabr.1998.7643.
   Web of Science ®Google Scholar
• Andruskiewitsch, N., Schneider, H.-J. (2002). Pointed Hopf algebras. In: Montgomery, S., Schneider, H.-J., eds. New Directions in Hopf Algebras. Mathematical Sciences Research Institute Publications, Vol. 43. Cambridge: Cambridge University Press, pp. 1–68.
   Google Scholar
• Andruskiewitsch, N., Schneider, H.-J. (2010). On the classification of finite-dimensional pointed Hopf algebras. Ann. Math. 171(1):375–417. DOI: 10.4007/annals.2010.171.375.
   Web of Science ®Google Scholar
• Chen, H., Oystaeyen, F. V., Zhang, Y. (2014). The Green rings of Taft algebras. Proc. Amer. Math. Soc. 142(3):765–775. DOI: 10.1090/S0002-9939-2013-11823-X.
   Web of Science ®Google Scholar
• Chen, J., Yang, S., Wang, D. (2021). Grothendieck rings of 2n2 dimensional Hopf algebras H2n2. Front. Math. China 16(1):29–47.
   Web of Science ®Google Scholar
• Ferraro, L., Kirkman, E., Moore, W. F., Won, R. (2020). Three infinite families of reflection Hopf algebras. J. Pure Appl. Algebra 224(8):106315. DOI: 10.1016/j.jpaa.2020.106315.
   Web of Science ®Google Scholar
• García, G. A., Giraldi, J. M. J., Matheus, J. G. J. (2019). On Hopf algebras over quantum subgroups. J. Pure Appl. Algebra 223(2):738–768. DOI: 10.1016/j.jpaa.2018.04.018.
   Web of Science ®Google Scholar
• Hu, N., Xiong, R. (2016). Some Hopf algebras of dimension 72 without the Chevalley property. arXiv:1612.04987.
   Google Scholar
• Kassel, C. (1995). Quantum Groups. New York: Springer.
   Google Scholar
• Kaplansky, I. (1975). Bialgebras. Lecture Notes in Mathematics. Chicago, IL: Department of Mathematics, University of Chicago.
   Google Scholar
• Kac, G. I., Paljutkin, V. G. (1966). Finite ring groups. Trudy Moskov. Mat. Obsˇcˇ. 15:224–261.
   Google Scholar
• Laugwitz, R. (2017). On Fomin-Kirillov algebras for complex reflection groups. Commun. Algebra 45(8):3653—3666. DOI: 10.1080/00927872.2016.1243698.
   Web of Science ®Google Scholar
• Li, L., Zhang, Y. (2013). The Green rings of the generalized Taft algebras. Con. Math. 585(10):275–288.
   Google Scholar
• Márquez, O., Bagio, D., Giraldi, J. M. J., García, G. A. (2021). Finite-dimensional Nichols algebras over dual Radford algebras. J. Algebra Appl. 20(1):2140001. DOI: 10.1142/S0219498821400016.
   Web of Science ®Google Scholar
• Masuoka, A. (1995). Semisimple Hopf algebras of dimension 6, 8. Isr. J. Math. 92(1–3):361–373. DOI: 10.1007/BF02762089.
   Web of Science ®Google Scholar
• Montgomery, S. (1993). Hopf Algebras and Their Actions on Rings. CMBS Regional Conference Series in Mathematics, Vol. 82. Providence, RI: American Mathematical Society.
   Google Scholar
• Pansera, D. (2019). A class of semisimple Hopf algebras acting on quantum polynomial algebras. In Rings, Modules and Codes. Contemp. Math. Vol. 727. Providence, RI: American Mathematical Society, pp. 303–316.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Shi, Y. (2019). Finite dimensional Nichols algebras over Kac-Paljutkin algebra H8. Revista de la Unión Matemàtica Argentina 60(1):265–298. DOI: 10.33044/revuma.v60n1a17.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Yetter, D. N. (1990). Quantum groups and representations of monoidal categories. Math. Proc. Cambridge Philos. Soc. 108(2):261–290.
   Web of Science ®Google Scholar
• Yang, S., Zhang, Y. (2020). Ore extensions for the Sweedler’s Hopf algebra H4. Mathematics 8(8):1293.
   Web of Science ®Google Scholar
• Zhu, H., Chen, H. (2012). Yetter-Drinfeld modules over the Hopf – Ore extension of the group algebra of dihedral group. Acta Math. Sin. Engl. Ser. 28(3):487–502. DOI: 10.1007/s10114-011-9777-4.
   Web of Science ®Google Scholar
• Zhang, Y. (2021). The ore extensions of Hopf algebras and their related topics. D. Beijing: Beijing University of Technology.
   Google Scholar