Physics – Mathematical Physics
Scientific paper
2009-02-06
J.Phys.A41:105203,2008
Physics
Mathematical Physics
27 pages, some typos of the journal version are corrected and a couple of references added
Scientific paper
Parabosonic algebra in finite or infinite degrees of freedom is considered as a $\mathbb{Z}_{2}$-graded associative algebra, and is shown to be a $\mathbb{Z}_{2}$-graded (or: super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the $osp(1/2n)$ Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category ${}_{\mathbb{CZ}_{2}}\mathcal{M}$. The bosonisation technique for switching a Hopf algebra in the braided monoidal category ${}_{H}\mathcal{M}$ (where $H$ is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper we prove that for the parabosonic algebra $P_{B}$, beyond the application of the bosonisation technique to the original super-Hopf algebra, a bosonisation-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra $P_{B}$ to an ordinary Hopf algebra, producing thus two different variants of $P_{B}$, with ordinary Hopf structure.
Daskaloyannis Costas
Kanakoglou Konstantinos
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