  In positive characteristic the Jordan plane covers a finite-dimensional
Nichols algebra that was described by Cibils, Lauve and Witherspoon and we call
the restricted Jordan plane. In this paper the characteristic is odd. The
defining relations of the Drinfeld double of the restricted Jordan plane are
presented and its simple modules are determined. A Hopf algebra that deserves
the name of double of the Jordan plane is introduced and various quantum
Frobenius maps are described. The finite-dimensional pre-Nichols algebras
intermediate between the Jordan plane and its restricted version are
classified. The defining relations of the graded dual of the Jordan plane are
given.
