On the Hopf-Schur group of a field

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Let k be any field. We consider the Hopf-Schur group of k, defined as the subgroup of the Brauer group of k consisting of classes that may be represented by homomorphic images of Hopf algebras over k. We show here that twisted group algebras and abelian extensions of k are quotients of cocommutative and commutative Hopf algebras over k, respectively. As a consequence we prove that any tensor product of cyclic algebras over k is a quotient of a Hopf algebra over k, revealing so that the Hopf-Schur group can be much larger than the Schur group of k.
12 pages, latex file

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Quantum Algebra, Representation Theory, 16W30

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http://salesiana.dossiersoluciones.com/handle/123456789/136071

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.1943
 http://arxiv.org/abs/0708.1943

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arXiv