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Jordan-Holder theorem for finite dimensional Hopf algebras

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 نشر من قبل Sonia Natale
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English
 تأليف Sonia Natale




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We show that a Jordan-Holder theorem holds for appropriately defined composition series of finite dimensional Hopf algebras. This answers an open question of N. Andruskiewitsch. In the course of our proof we establish analogues of the Noether isomorphism theorems of group theory for arbitrary Hopf algebras under certain faithful (co)flatness assumptions. As an application, we prove an analogue of Zassenhaus butterfly lemma for finite dimensional Hopf algebras. We then use these results to show that a Jordan-Holder theorem holds as well for lower and upper composition series, even though the factors of such series may be not simple as Hopf algebras.



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