  We construct explicit Drinfel'd twists of Jordanian type for the generalized
Cartan type K Lie algebras in characteristic 0 and obtain the corresponding
quantizations, especially their integral forms. By making modular reductions
including modulo p and modulo p-restrictedness reduction, and base changes, we
derive certain modular quantizations of the restricted universal enveloping
algebra $\mathbf u(\mathbf{K}(2n{+}1;\underline{1}))$ for the restricted simple
Lie algebra of Cartan type K in characteristic p. They are new pointed Hopf
algebras of noncommutative and noncocommutative and with dimension
$p^{p^{2n+1}+1}$ (if $2n+4\not\equiv0 \; (\mod p)$) or $p^{p^{2n+1}}$ (if
$2n+4\equiv0 \; (\mod p))$ over a truncated p-polynomials ring, which also
contain the well-known Radford algebras as Hopf subalgebras. Some open
questions are proposed.

Quantum Algebra