International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 28, Pages 1477-1486
doi:10.1155/S016117120430236X
Twisted quantum doubles
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.
Abstract
Using diagrammatic pictures of tensor contractions, we consider a Hopf algebra (Aop⊗ℛλA*)* twisted by an element ℛλ∈A*⊗Aop
corresponding to a Hopf algebra morphism λ:A→A. We show that this Hopf algebra is quasitriangular with the universal R-matrix coming from ℛλ when λ2=idA, generalizing the quantum double construction which corresponds to the case λ=idA.