  We give a new, conceptual proof of the $\imath$Serre and Serre-Lusztig
relations for $\imath$quantum groups. The key to our approach is a new formula
for the comultiplication of the $\imath$-divided powers, which allows us to
reformulate the relations in terms of the adjoint action. We then obtain a
proof using properties of the adjoint representation. The flexibility of this
approach allows us to establish a more general family of relations which seem
difficult to establish otherwise.
