On the existence of orders in semisimple Hopf algebras

Juan Cuadra, Ehud Meir

Research output: Contribution to journalArticle

4 Citations (Scopus)
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Abstract

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 Drinfel'd 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 Kaplansky's sixth conjecture if and only if it admits a weak order, in the sense of Rumynin and Lorenz, over the integers.
Original languageEnglish
Pages (from-to)2547-2562
Number of pages16
JournalTransactions of the American Mathematical Society
Volume368
Issue number4
Early online date20 Aug 2015
DOIs
Publication statusPublished - Apr 2016

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Hopf Algebra
Semisimple
Twist
Ring
Weak Order
Definability
Group Algebra
Scalar
If and only if
Integer

Cite this

On the existence of orders in semisimple Hopf algebras. / Cuadra, Juan; Meir, Ehud.

In: Transactions of the American Mathematical Society, Vol. 368, No. 4, 04.2016, p. 2547-2562.

Research output: Contribution to journalArticle

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