Assume Q is a quantum Lie group which allows a R matrix (with the usual
quantum Yang-Baxter equation). 
Take the Jordan normal form J of R. Does a Q exist with offdiagonal J elements
(i.e. R has defective eigenvalues)? 



A property of quantum group R matrices?
What is meant by a Quantum Lie Group here?


If we are talking about the quantized enveloping algebras of complex semisimple lie algebras $U\_q(\mathfrak{g})$ then it is a fact that the action of the universal $R$-matrix on the tensor product of finite dimensional representations is semisimple i.e. its Jordan form is diagonal


