On the Hopf-Schur group of a field

Eli Aljadeff, Juan Cuadra, Shlomo Gelaki*, Ehud Meir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish
Pages (from-to)5165-5177
Number of pages13
JournalJournal of Algebra
Volume319
Issue number12
DOIs
StatePublished - 15 Jun 2008

Keywords

  • Brauer group
  • Hopf algebras
  • Hopf-Schur group
  • Projective group

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