A very easy question I can't seem to answer: For a universal r-form on a co-quasi-triangular Hopf algebra why is $r(a \otimes 1) = r(1 \otimes a) = \epsilon(a)$?



Action of  Co-quasi-triangular Universal r-form on $a \otimes 1$
Like David said, the proof is almost identical to the earlier one for $R$-matrices:


$r(x\otimes 1) = r\circ (id\otimes\mu)(x\otimes 1\otimes 1) = (r\_{13}\ast r\_{12})(x\otimes 1\otimes1)= \sum r(x'\otimes 1)r(x''\otimes 1) = (r \ast r)(x\otimes 1).$


Since $r$ is invertible, $r(x\otimes 1)=\epsilon(x)$.


