Twists and quantizations of Cartan type S Lie algebras

We construct explicit Drinfel’d twists for the generalized Cartan type Lie algebras and obtain the corresponding quantizations. By modular reduction and base changes, we obtain certain quantizations of the restricted universal enveloping algebra in characteristic p. They are new Hopf algebras of truncated p-polynomial noncommutative and noncocommutative deformation of dimension p1+(n−1)(pn−1), which contain the well-known Radford algebra (Radford (1977) [23]) as a Hopf subalgebra. As a by-product, we also get some Jordanian quantizations for sln.