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On the existence of orders in semisimple Hopf algebras

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 نشر من قبل Juan Cuadra
 تاريخ النشر 2013
  مجال البحث
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We show that there is a family of complex semisimple Hopf algebras that do not admit a Hopf order over any number ring. They are Drinfeld twists of certain group algebras. The twist contains a scalar fraction which makes impossible the definability of such Hopf algebras over number rings. We also prove that a complex semisimple Hopf algebra satisfies Kaplanskys sixth conjecture if and only if it admits a weak order, in the sense of Rumynin and Lorenz, over the integers.



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