Parabosonic and parafermionic algebras. Graded structure and Hopf structures

Abstract

Parabosonic $P_{B}^{(n)}$ and parafermionic $P_{F}^{(n)}$ algebras are described as quotients of the tensor algebras of suitably choosen vector spaces. Their (super-) Lie algebraic structure and consequently their (super-) Hopf structure is shortly discussed. A bosonisation-like construction is presented, which produces an ordinary Hopf algebra $P_{B(K^{\pm})}^{(n)}$ starting from the super Hopf algebra $P_{B}^{(n)}$.