 
Summary: Journal of Algebra 319 (2008) 51655177
www.elsevier.com/locate/jalgebra
On the HopfSchur group of a field
Eli Aljadeff a
, Juan Cuadra b
, Shlomo Gelaki a,
, Ehud Meir a
a Department of Mathematics, TechnionIsrael Institute of Technology, Haifa 32000, Israel
b Departamento de Álgebra y Análisis Matemático, Universidad de Almería, E04120 Almería, Spain
Received 17 August 2007
Available online 12 February 2008
Communicated by Nicolás Andruskiewitsch
Abstract
Let k be any field. We consider the HopfSchur group of k, defined as the subgroup of the Brauer group
of k consisting of classes that may be represented by homomorphic images of finitedimensional Hopf
algebras over k. We show here that twisted group algebras and abelian extensions of k are quotients of
cocommutative and commutative finitedimensional Hopf algebras over k, respectively. As a consequence
we prove that any tensor product of cyclic algebras over k is a quotient of a finitedimensional Hopf algebra
over k, revealing so that the HopfSchur group can be much larger than the Schur group of k.
© 2008 Elsevier Inc. All rights reserved.
