Serre-Lusztig relations for $imath$quantum groups

Let $(bf U, bf U^imath)$ be a quantum symmetric pair of Kac-Moody type. The $imath$quantum groups $bf U^imath$ and the universal $imath$quantum groups $widetilde{bf U}^imath$ can be viewed as a generalization of quantum groups and Drinfeld doubles $widetilde{bf U}$. In this paper we formulate and establish Serre-Lusztig relations for $imath$quantum groups in terms of $imath$divided powers, which are an $imath$-analog of Lusztigs higher order Serre relations for quantum groups. This has applications to braid group symmetries on $imath$quantum groups.