A nonlinear deformed su(2) algebra with a two-color quasitriangular Hopf structure (Q2785756)

Some nonlinear deformations (Delbecq, Quesne, 1994) of the universal enveloping algebra of \(\text{su}(2)\), involving two arbitrary functions of the algebra generator \(J_0\) and generalizing the Witten algebra, are endowed with a Hopf structure. A specific example of the Delbecq-Quesne algebra \({\mathcal A}_q^+(1)\), possessing two series of \(N+1\)-dimensional \((N=0,1,2,\dots)\) unitary irreducible representations is studied in detail. To allow the coupling of any two such representations, a generalization of standard Hopf axioms is proposed. As a result, the Hopf structure of \(\text{su}_q(2)\) is carried over to \({\mathcal A}_q^+(1)\), endowing the latter with double Hopf structure. At last, the Hopf algebra is enlarged into a new algebraic structure, which is referred to as a two-color quasitriangular Hopf algebra. The corresponding \(R\)-matrix is a solution of the colored Yang-Baxter equation, where the ``color'' parameters take two discrete values associated with the above two series of finite-dimensional representations of the algebra \({\mathcal A}_q^+(1)\).