On Automorphisms and Universal R-Matrices at Roots of Unity
Abstract
Invertible universal R-matrices of quantum Lie algebras do not exist at roots of unity. There exist however quotients for which intertwiners of tensor products of representations always exist, i.e. R-matrices exist in the representations. One of these quotients, which is finite dimensional, has a universal R-matrix. In this paper, we answer the following question: on which condition are the different quotients of U_q(sl(2)) (Hopf)-equivalent? In the case when they are equivalent, the universal R-matrix of one can be transformed into a universal R-matrix of the other. We prove that this happens only when q^4=1, and we explicitly give the expressions for the automorphisms and for the transformed universal R-matrices in this case.
Cite
@article{arxiv.hep-th/9403110,
title = {On Automorphisms and Universal R-Matrices at Roots of Unity},
author = {Daniel Arnaudon},
journal= {arXiv preprint arXiv:hep-th/9403110},
year = {2009}
}
Comments
11 pages, minor TeXnical revision to allow automatic TeXing