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Parabosonic algebra in infinite degrees of freedom is presented as ageneralization of the bosonic algebra, from the viewpoints of both physics andmathematics. The notion of super-Hopf algebra is shortly discussed and thesuper-Hopf algebraic structure of the parabosonic algebra is established(without appealing to its Lie superalgebraic structure). Two possible variantsof the parabosonic algebra are presented and their (ordinary) Hopf algebraicstructure is estabished: The first is produced by "bosonising" the originalsuper-Hopf algebra, while the second is constructed via a slightly differentpath.

Graded structure and Hopf structures in parabosonic algebra. An alternative approach to bosonisation