  The aim of this paper is to show that there is a Hopf structure of the
parabosonic and parafermionic algebras and this Hopf structure can generate the
well known Hopf algebraic structure of the Lie algebras, through a realization
of Lie algebras using the parabosonic (and parafermionic) extension of the
Jordan Schwinger map. The differences between the Hopf algebraic and the graded
Hopf superalgebraic structure on the parabosonic algebra are discussed.
