\nonumber \\
&& -(\alpha_1+2)\hat{M}_{i0}p_ip_j\otimes p_j +(\beta_1+2)p_j\otimes \hat{M}_{i0}p_ip_j +\alpha_1\hat{M}_{i0}p_jp_j\otimes p_i -\beta_1p_i\otimes \hat{M}_{i0}p_jp_j \nonumber \\
&& -2\hat{M}_{i0}\otimes p_ip_jp_j +2p_ip_jp_j\otimes \hat{M}_{i0} +3\hat{M}_{i0}p_0^2\otimes p_i -3p_i\otimes \hat{M}_{i0}p_0^2 \nonumber \\
&& +2\hat{M}_{i0}p_0\otimes p_ip_0 -2p_ip_0\otimes \hat{M}_{i0}p_0 +3\hat{M}_{i0}\otimes p_ip_0^2 -3p_ip_0^2\otimes \hat{M}_{i0} \nonumber \\
&& -(\alpha_2+2)\hat{M}_{i0}p_i\otimes p_jp_j +(\alpha_2+2)p_jp_j\otimes \hat{M}_{i0}p_i \nonumber \\
&& +(\alpha_2+2)\hat{M}_{i0}p_j\otimes p_ip_j -(\alpha_2+2)p_ip_j\otimes \hat{M}_{i0}p_j \Bigr).\end{aligned}$$ If we choose $\alpha_1=\beta_1$, we get a two-parameter family of solutions for $r_3$, which all have a wedge-product structure. $r_1, \,r_2$ and the special case of $r_3$ with $\alpha_1=\beta_1=-6, \, \alpha_2=-2$ coincide with the results found in [@Young:2008zm].

Analogously, the $R$-matrix can be expanded in the generators $p_\mu$ and $M_{\mu \nu}$ (from the case (i) in Section \[IV\]). However, an easier way is to insert the known relation [@Kovacevic:2012an] between $M$ (for $\lambda=1/2$) and $\hat{M}$ ($\hat{M}_{i0}=M_{i0}Z^{-\frac{1}{2}}+\frac{a_0}{2}M_{ij}p_j, \, \hat{M}_{ij}=M_{ij}$) into the results presented above.

Contrary to $M$, the generators $\widetilde{M}$, from the case (iii) in Section \[IV\], cannot be related to $\hat{M}$ (see Ref.[@Kovacevic:2012an]). Consequently, the universal $R$-matrix cannot be expanded in $\widetilde{M}$ and $p$. One arrives at the same result when trying to repeat the presented procedure with $\widetilde{M}$ instead of $\hat{M}$ (the system of equations for the coefficients of $r_3$ doesn’t have a solution). The above conclusions can be easily extended 