Jordan-Hölder theorem for finite dimensional Hopf algebras

SONIA NATALE

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2015 vol. 143 p. 5195 - 5211

0002-9939

We show that a Jordan-H ̈older 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 p roof 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-H ̈older theorem holds as well for lower and upper composition series, even though the factors of such series may be not simple as Hopf algebras