Some bismash products that are not group algebras II

We study several families of semisimple Hopf algebras, arising as bismash products, which are constructed from finite groups with a certain specified factorization. First we associate a bismash product H q of dimension q(q − 1)(q + 1) to each of the finite groups PGL 2 (q) and show that these H q do not have the structure (as algebras) of group algebras (except when q = 2, 3). As a corollary, all Hopf algebras constructed from them by a comultiplication twist also have this property and are thus non-trivial. We also show that bismash products constructed from Frobenius groups do have the structure (as algebras) of group algebras.

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Some bismash products that are not group algebras II

Cited by 2 publications

References 11 publications

Crossed Products as Twisted Category Algebras

Crossed Products as Twisted Category Algebras

On the algebra structure of some bismash products

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