We construct convex PBW-type Lyndon bases for two-parameter quantum groups U_{ r,s}({ so}_{ 2n+1}) with detailed commutation relations. It turns out that under a certain condition, the restricted two-parameter quantum group u_{ r,s}({ so}_{ 2n+1}) (r, s are roots of unity) is of Drinfeld double. All of Hopf isomorphisms of u_{ r,s}({ so}_{ 2n+1}), as well as u_{ r,s}({ sl}_n) are determined. Finally, necessary and sufficient conditions for u_{ r,s}({ so}_{ 2n+1}) to be a ribbon Hopf algebra are singled out by describing the left and right integrals.
Categories: math.QA math.RT