Multi-parametric q-deformation of the SO(5) Algebra: With deSitter in Mind

We start with the idea that the Drinfeld-Jimbo(DJ) quantum algebras for the classical groups can be generated using R-matrices in the Faddeev-ReshetikhinTakhtadzhyan(FRT) formalism. But instead of using it to the case of the one-parameter R-matrix to generate the usual Drinfeld-Jimbo algebras, we apply the FRT approach to a multi-parametric R-matrix. Specifically, we apply it to the two-parametric R-matrix of SO(5), because this is a case that could have implications when doing quantum mechanics in deSitter space. We write down the explicit form of the multi-parametric DJ algebra for SO(5) and notice that it goes to the usual SO(5) DJ algebra when the parameters become degenerate.