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Journal of Algebra 319 (2008) 51655177 www.elsevier.com/locate/jalgebra
 

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, Technion-Israel 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 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 Hopf­Schur group can be much larger than the Schur group of k.
© 2008 Elsevier Inc. All rights reserved.

  

Source: Aljadeff, Eli - Department of Mathematics, Technion, Israel Institute of Technology

 

Collections: Mathematics