 
Summary: Journal of Algebra 256 (2002) 484501
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On twisting of finitedimensional Hopf
algebras
Eli Aljadeff,a
Pavel Etingof,b,
Shlomo Gelaki,a
and Dmitri Nikshych c
a Department of Mathematics, TechnionIsrael Institute of Technology, Haifa 32000, Israel
b Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
c Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA
Received 24 July 2001
Communicated by Susan Montgomery
Abstract
In this paper we study the properties of Drinfeld's twisting for finitedimensional Hopf
algebras. We determine how the integral of the dual to a unimodular Hopf algebra H
changes under twisting of H. We show that the classes of cosemisimple unimodular,
cosemisimple involutive, cosemisimple quasitriangular finitedimensional Hopf algebras
are stable under twisting. We also prove the cosemisimplicity of a coalgebra obtained by
twisting of a cosemisimple unimodular Hopf algebra by two different twists on two sides
