Algebraic structures and new solutions of the Yang-Baxter equation

Let G be a semisimple (or reductive) Lie algebra or a classical simple Lie superalgebra, then its universal enveloping algebra U(G) is a Hopf (super-)algebra under the standard (super-)cocommutative coproduct Delta(x) = x x 1 + 1 x x, x is an element of G. The Hopf (super-)algebra U(G) is triangular with R-matrix R = 1 x 1. There exist many other non-(super-)cocommutative coproducts on U(G) (and therefore many distinct Hopf (super-)algebra structures). These new Hopf (super-)algebras are quasitriangular, and with the new coproducts are associated new R-matrices. It is the aim of this paper to present a construction of new coproducts and a determination of the corresponding R-matrices.