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 $P_B^{(n)}$.

9 pages. Contribution to the 6th Paanhellenic conference in Algebra and Number Theory, Aristotle University of Thessaloniki, Thessaloniki, 10-12 June 2006