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We give a new, conceptual proof of the $\imath$Serre and Serre-Lusztigrelations for $\imath$quantum groups. The key to our approach is a new formulafor the comultiplication of the $\imath$-divided powers, which allows us toreformulate the relations in terms of the adjoint action. We then obtain aproof using properties of the adjoint representation. The flexibility of thisapproach allows us to establish a more general family of relations which seemdifficult to establish otherwise.

A new approach to the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups