On the Hopf-Schur group of a field

Details On the Hopf-Schur group of a field On the Hopf-Schur group of a field

2007-08-14

arxiv.org/abs/0708.1943v1

Mathematics

Quantum Algebra

12 pages, latex file

Scientific paper

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.

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