Cocycle deformations and Galois objects of semisimple Hopf algebras of dimension 16

References

• Benkart, G., Pereira, M., Witherspoon, S. (2010). Yetter-Drinfeld modules under cocycle twists. J. Algebra 324(11):2990–3006. DOI: 10.1016/j.jalgebra.2009.10.001.
   Web of Science ®Google Scholar
• Castano, A. M., Montgomery, S., Natale, S., Vega, M. D., Walton, C. (2018). Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension p3 and pq2. J. Pure Appl. Algebra 222(7):1643–1669. DOI: 10.1016/j.jpaa.2017.07.016.
   Web of Science ®Google Scholar
• Enock, M., Vainerman, L. (1996). Deformation of the Kac algebra by an abelian subgroup. Commun. Math. Phys. 178(3):571–596. DOI: 10.1007/BF02108816.
   Web of Science ®Google Scholar
• Etingof, P., Gelaki, S., Nikshych, D., Ostrik, V. (2015). Tensor Categories. AMS Mathematical Surveys and Monographs, Vol. 205. Providence, RI: American Mathematical Society.
   Google Scholar
• Etingof, P., Nikshych, D., Ostrik, V. (2005). On fusion categories. Ann. Math. 162(2):581–642. DOI: 10.4007/annals.2005.162.581.
   Web of Science ®Google Scholar
• Etingof, P., Nikshych, D., Ostrik, V. (2011). Weakly group-theoretical and solvable fusion categories. Adv. Math. 226:176–205.
   Web of Science ®Google Scholar
• Hofstetter, I. (1994). Extensions of Hopf algebras and their cohomological description. J. Algebra 164(1):264–298. DOI: 10.1006/jabr.1994.1063.
   Web of Science ®Google Scholar
• Huang, H., Liu, G., Yang, Y., Ye, Y. (2020). Finite quasi-quantum groups of diagonal type. J. Reine Angew. Math. 759:201–243.
   Web of Science ®Google Scholar
• Kac, G. I. (1968). Extensions of groups to ring groups. Math. USSR. Sb. 5(3):451–474. DOI: 10.1070/SM1968v005n03ABEH003627.
   Google Scholar
• Karpilovsky, G. (1987). The Schur Multiplier. Oxford University Press. London Mathematical Society Monographs. New Series, 2. New York: The Clarendon Press, Oxford University Press.
   Google Scholar
• Kashina, Y. (2000). Classification of semisimple Hopf algebras of dimension 16. J. Algebra 232(2):617–663. DOI: 10.1006/jabr.2000.8409.
   Web of Science ®Google Scholar
• Kashina, Y., Mason, G., Montgomery, S. (2002). Computing the Frobenius-Schur indicator for abelian extensions of Hopf algebras. J. Algebra 251(2):888–913. DOI: 10.1006/jabr.2001.9129.
   Web of Science ®Google Scholar
• Kashina, Y., Sommerhäuser, Y., Zhu, Y. (2006). On higher Frobenius-Schur indicators. Mem. Amer. Math. Soc. 181(855):viii+65 pp. DOI: 10.1090/memo/0855.
   Web of Science ®Google Scholar
• Linchenko, V., Montgomery, S. (2000). A Frobenius-Schur theorem for Hopf algebras. Algebra Represent. Theory 3(4):347–355. DOI: 10.1023/A:1009949909889.
   Google Scholar
• Mason, G., Ng, S. H. (2005). Central invariants and Frobenius-Schur indicators for semisimple quasi-Hopf algebras. Adv. Math. 190(1):161–195. DOI: 10.1016/j.aim.2003.12.004.
   Web of Science ®Google Scholar
• Masuoka, A. (1995). Self-dual Hopf algebras of dimension p3 obtained by extension. J. Algebra 178(3):791–806. DOI: 10.1006/jabr.1995.1378.
   Web of Science ®Google Scholar
• Masuoka, A. (2000). Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension. New trends in Hopf algebra theory, 195–214, Contemp. Math., 267. Providence, RI: Amer. Math. Soc.
   Google Scholar
• Masuoka, A. (2002). Hopf algebra extensions and cohomology. Math. Sci. Res. Inst. Publ. 43:167–209.
   Google Scholar
• Natale, S. (1999). On semisimple Hopf algebras of dimension pq2. J. Algebra 221(1):242–278. DOI: 10.1006/jabr.1999.7968.
   Web of Science ®Google Scholar
• Natale, S. (2001). On semisimple Hopf algebras of dimension pq2 II. Algebr. Reprsent. Theory 4(3):277–291.
   Web of Science ®Google Scholar
• Natale, S. (2003). On group theoretical Hopf algebras and exact factorizations of finite groups. J. Algebra 270:199–211.
   Web of Science ®Google Scholar
• Natale, S. (2017). On the equivalence of module categories over a group-theoretical fusion category. SIGMA. 13(042):9. DOI: 10.3842/SIGMA.2017.042.
   Google Scholar
• Ng, S.-H., Schauenburg, P. (2007). Central invariants and higher indicators for semisimple quasi-Hopf algebras. Trans. Amer. Math. Soc. 360(04):1839–1860. DOI: 10.1090/S0002-9947-07-04276-6.
   Google Scholar
• Ng, S.-H., Schauenburg, P. (2007). Frobenius-Schur indicators and exponents of spherical categories. Adv. Math. 211:34–71.
   Web of Science ®Google Scholar
• Nikshych, D. (1998). K0-rings and twisting of finite-dimensional semisimple Hopf algebras. Commun. Algebra 26(1):321–342; Erratum: (1998) K0-rings and twisting of finite-dimensional semisimple Hopf algebras, Commun. Algebra 26(4), 1347. DOI: 10.1080/00927879808826132.
   Web of Science ®Google Scholar
• Ostrik, V. (2003). Module categories, weak Hopf algebras and modular invariants. Transform. Groups 8(2):177–206. DOI: 10.1007/s00031-003-0515-6.
   Web of Science ®Google Scholar
• Ostrik, V. (2003). Module categories over the Drinfeld double of a finite group. Int. Math. Res. Not. 2003(27):1507–1520.
   Web of Science ®Google Scholar
• Schauenburg, P. (1996). Hopf bi-Galois extensions. Commun. Algebra 24(12):3797–3825. DOI: 10.1080/00927879608825788.
   Web of Science ®Google Scholar
• Ulbrich, K. H. (1987). Galois extensions as functors of comodules. Manuscripta Math. 59(4):391–397. DOI: 10.1007/BF01170844.
   Web of Science ®Google Scholar