Extensions of finite quantum groups by finite groups

Details Extensions of finite quantum groups by finite groups Extensions of finite quantum groups by finite groups

2006-08-26

arxiv.org/abs/math/0608647v7

Transformation Groups Vol. 14, N. 1 (March 2009). Pages 1-27

Mathematics

Quantum Algebra

final version, to appear in Transformation Groups

Scientific paper

We give a necessary and sufficient condition for two Hopf algebras presented as central extensions to be isomorphic, in a suitable setting. We then study the question of isomorphism between the Hopf algebras constructed in 0707.0070v1 as quantum subgroups of quantum groups at roots of 1. Finally, we apply the first general result to show the existence of infinitely many non-isomorphic Hopf algebras of the same dimension, presented as extensions of finite quantum groups by finite groups.

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