On Hopf algebras over the unique 12-dimensional Hopf algebra without the dual Chevalley property

References

• Andruskiewitsch, N., Angiono, I.-E. (2018). On Nichols algebras over basic Hopf algebras. arXiv:1802.00316.
   Google Scholar
• Andruskiewitsch, N., Beattie, M. (2004). Irreducible representations of liftings of quantum planes. In: Lie Theory and Its Applications in Physics V. River Edge, NJ: World Scientific, pp. 414–423.
   Google Scholar
• Andruskiewitsch, N., Cuadra, J. (2013). On the structure of (co-Frobenius) hopf algebras. J. Noncommut. Geom. 7(1): 83–104.
   Web of Science ®Google Scholar
• Andruskiewitsch, N., Giraldi, J.-M.-J. (2018). Nichols algebras that are quantum planes. Linear Multilinear Algebra 66(5): 961–991.
   Web of Science ®Google Scholar
• Andruskiewitsch, N., Gra, M. (1999). Braided hopf algebras over non abelian finite group. Bol. Acad. Nac. Cienc. Cordoba 63:46–78.
   Google Scholar
• Andruskiewitsch, N., Heckenberger, I., Schneider, H.-J. (2010). The Nichols algebra of a semisimple Yetter-Drinfeld module. Am. J. Math. 132(6):1493–1547.
   Web of Science ®Google Scholar
• Andruskiewitsch, N., Schneider, H.-J. (1998). Lifting of quantum linear spaces and pointed hopf algebras of order p3. J. Algebr. 209(2): 658–691.
   Web of Science ®Google Scholar
• Andruskiewitsch, N., Schneider, H.-J. (2002). Pointed Hopf Algebras, New Directions in Hopf Algebras, 1–68. Cambridge, MA: Cambridge Univ. Press,
   Google Scholar
• Auslander, M., Reiten, I., Smalø, S.-O. (1995). Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics, 36. Cambridge, MA: Cambridge University Press.
   Google Scholar
• Beattie, M., Garcia, G.-A. (2013). Classifying Hopf algebras of a given dimension. Contemp. Math. 585: 125–152.
   Google Scholar
• Bergman, G. (1978). The diamond lemma for ring theory. Adv. Math. 29(2): 178–218.
   Web of Science ®Google Scholar
• Chen, H., Mohammed, H., Lin, W., Sun, H. (2017). The projective class rings of a family of pointed Hopf algebras of rank two. arXiv:1709.08782.
   Google Scholar
• Garcia, G.-A., Giraldi, J. M. J. (2019). On Hopf algebra over quantum subgroups. J. Pure Appl. Algebra 223: 738–768. DOI:10.1016/j.jpaa.2018.04.018.
   Web of Science ®Google Scholar
• Graña, M. (2000). Freeness theorem for Nichols algebras. J. Algebra 231(1):235–257.
   Web of Science ®Google Scholar
• Grunenfelder, L., Mastnak, M. (2010). Pointed Hopf algebras as cocycle deformations. arXiv:1010.4976.
   Google Scholar
• Heckenberger, I. (2009). Classification of arithmetic root systems. Adv. Math. 220(1): 59–124.
   Web of Science ®Google Scholar
• Hietarinta, J. (1993). Solving the two-dimensional constant quantum Yang-Baxter equation. J. Math. Phys. 34(5): 1725–1756.
   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
• Hu, N., Xiong, R. (2018). On families of Hopf algebras without the dual Chevalley property. Revis. Unión Matemática Argentina. 59(2): 443–469.
   Web of Science ®Google Scholar
• Iglesias, A.-G. (2010). Representations of pointed Hopf algebras over S3. Revis. Unión Matemática Argentina 51: 51–77.
   Web of Science ®Google Scholar
• Majid, S., Oeckl, R. (1999). Twisting of quantum differentials and the planck scale Hopf algebra. Comm. Math. Phys. 205(3): 617–655.
   Web of Science ®Google Scholar
• Montgomery, S. (1993). Hopf Algebras and Their Actions on Rings. CMBS Regional Conference Series in Mathematics 82. Providence, RI: American Mathematical Society.
   Google Scholar
• Natale, S. (2002). Hopf algebras of dimension 12. Algebra Represent. Theory 5(5): 445–455.
   Web of Science ®Google Scholar
• Nichols, W.-D. (1978). Bialgebras of type one. Commun. Algebra 6(15): 1521–1552.
   Web of Science ®Google Scholar
• Radford, D.-E. (1975). On the coradical of a finite-dimensional Hopf algebra. Proc. Am. Math. Soc. 53(1): 9–15.
   Web of Science ®Google Scholar
• Radford, D.-E. (1985). The structure of Hopf algebras with a projection. J. Algebra 92(2): 322–347.
   Web of Science ®Google Scholar
• Radford, D.-E. (2011). Hopf Algebras, Knots and Everything 49. Singapore: World Scientific.
   Google Scholar
• Xiong, R. (2018). Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra. arXiv:1801.06205.
   Google Scholar