Universal \(R\)-matrix for quantized (super)algebras (Q1180370)

The authors give an explicit formula, in terms of \(q\)-exponentials, for the universal \(R\)-matrix of quantized finite-dimensional Lie superalgebras. To do this, one must be able to define arbitrary root vectors in the quantum algebra. In the non-super case, this can be done by using the action of a braid group, but in the super case no analogue of this is known, and is unlikely to exist since, even in the classical case, Lie superalgebras do not have good Weyl groups. Thus, the main novelty in this paper is a new method of defining root vectors.