Let be an odd prime number and a number field having a primitive th root of unity . We prove that Nikshych's non group-theoretical Hopf algebra , which is defined over , admits a Hopf order over the ring of integers if and only if there is an ideal of such that . This condition does not hold in a cyclotomic field. Hence this gives an example of a semisimple Hopf algebra over a number field not admitting a Hopf order over any cyclotomic ring of integers. Moreover, we show that, when a Hopf order over exists, it is unique and we describe it explicitly.
Cite this article
Juan Cuadra, Ehud Meir, Orders of Nikshych's Hopf algebra. J. Noncommut. Geom. 11 (2017), no. 3, pp. 919–955DOI 10.4171/JNCG/11-3-5