A Drinfeld type presentation of twisted Yangians of quasi-split type

In this paper, we formulate a family of algebras, twisted Yangians (of simply-laced quasi-split type) in Drinfeld type current generators and defining relations. These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras. For all quasi-split types excluding the even rank case in type AIII, we show that the twisted Yangians can be realized via a degeneration on the Drinfeld type presentation of affine [Formula: see text]quantum groups. For both even and odd rank cases in type AIII, we use the Gauss decomposition method to show that these new algebras are isomorphic to Molev–Ragoucy’s reflection algebras defined in the [Formula: see text]-matrix presentation.