Tetrahedron equation and generalized quantum groups

We construct 2ⁿ-families of solutions of the YangBaxter equation from nproducts of three-dimensional R and L operators satisfying the tetrahedron equation. They are identified with the quantum R matrices for the Hopf algebras known as generalized quantum groups. Depending on the number of 1's and L's involved in the product, the trace construction interpolates the symmetric tensor representations of U_q (A_n-1⁽¹⁾) and the antisymmetric tensor representations of U_-q^-1 (A_n-1⁽¹⁾), whereas a boundary vector construction interpolates the q-oscillator representation of Uq (Dn 1) (2) + and the spin representation of U_q (D_n+1⁽²⁾) . The intermediate cases are associated with an affinization of quantum superalgebras.