Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan–Schwinger map

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...

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Veröffentlicht in:Journal of mathematical physics 2000-02, Vol.41 (2), p.652-660
Hauptverfasser: Daskaloyannis, C., Kanakoglou, K., Tsohantjis, I.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.533157