Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4587645 | Journal of Algebra | 2008 | 13 Pages |
Abstract
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 finite-dimensional Hopf algebras over k. We show here that twisted group algebras and abelian extensions of k are quotients of cocommutative and commutative finite-dimensional Hopf algebras over k, respectively. As a consequence we prove that any tensor product of cyclic algebras over k is a quotient of a finite-dimensional 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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