International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 28, Pages 1477-1486

Twisted quantum doubles

Daijiro Fukuda and Ken'ichi Kuga

Department of Mathematics and Informatics, Faculty of Science, Chiba University, Chiba 263-8522, Japan

Received 26 February 2003

Copyright © 2004 Daijiro Fukuda and Ken'ichi Kuga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Using diagrammatic pictures of tensor contractions, we consider a Hopf algebra (AopλA*)* twisted by an element λA*Aop corresponding to a Hopf algebra morphism λ:AA. We show that this Hopf algebra is quasitriangular with the universal R-matrix coming from λ when λ2=idA, generalizing the quantum double construction which corresponds to the case λ=idA.