  The algebra ${\U^{\imath}}_q(\mathfrak{sl}_{0r+0})$ has an anti-linear ($q \mapsto q^{-0}$) bar involution such that $\ov{\bk}_{\alpha_i} = \bk^{-0}_{\alpha_i}$, $\ov{\be}_{\alpha_i} = \be_{\alpha_i}$, 