Lax operator for the quantized orthosymplectic superalgebraUq[osp(2|n)

Abstract

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains auniversal R-matrix in the tensor product algebra which satisfies theYang–Baxter equation. Applying the vector representationπ, which acts on thevector module V, toone side of a universal R-matrix gives a Lax operator. In this paper a Lax operator is constructed for theC-type quantumsuperalgebras Uq[osp(2|n)]. This is achieved without reference to the specific details of the universalR-matrix, but instead appealing to the co-product structure ofUq[osp(2|n)]. The result can in turn be used to find a solution to the Yang–Baxter equation acting on , where W isan arbitrary Uq[osp(2|n)] module. The case W = V is included here as an example.