Super-Hopf realizations of Lie superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map
- Instituto de Fisica y Matematicas (IFM), Universidad Michoacana de San Nicolas de Hidalgo (UMSNH), Edificio C-3, Cd. Universitaria, CP 58040, Morelia, Michoacan (Mexico)
- School of Mathematics, Analysis Department, Aristotle University of Thessaloniki (AUTH), 54124 Thessaloniki (Greece)
The mathematical structure of a mixed paraparticle system (combining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be described for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it will be shown that these realizations possess the valuable representation-theoretic property of transferring invariably the super-Hopf structure. Finally two classes of virtual applications will be outlined: The first is of interest for both mathematics and mathematical physics and deals with the representation theory of infinite dimensional Lie superalgebras, while the second is of interest in theoretical physics and has to do with attempts to determine specific classes of solutions of the Skyrme model.
- OSTI ID:
- 21415276
- Journal Information:
- AIP Conference Proceedings, Vol. 1256, Issue 1; Conference: 8. Mexican school on gravitation and mathematical physics, Playa del Carmen, Quintana Roo (Mexico), 6-12 Dec 2009; Other Information: DOI: 10.1063/1.3473853; (c) 2010 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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