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.
Original language | English |
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Pages (from-to) | 5165-5177 |
Number of pages | 13 |
Journal | Journal of Algebra |
Volume | 319 |
Issue number | 12 |
DOIs | |
State | Published - 15 Jun 2008 |
Externally published | Yes |
Keywords
- Brauer group
- Hopf algebras
- Hopf-Schur group
- Projective group