Super-Hopf realizations of Lie superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map
Abstract
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.
- Publication:
-
Gravitational Physics: Testing Gravity from Submillimeter to Cosmic
- Pub Date:
- July 2010
- DOI:
- 10.1063/1.3473853
- arXiv:
- arXiv:1008.0680
- Bibcode:
- 2010AIPC.1256..193K
- Keywords:
-
- Lie algebras;
- skyrmions;
- boson systems;
- functional analysis;
- matrix algebra;
- 02.20.Sv;
- 12.39.Dc;
- 05.30.Jp;
- 02.30.Sa;
- 02.10.Yn;
- Lie algebras of Lie groups;
- Skyrmions;
- Boson systems;
- Functional analysis;
- Matrix theory;
- Mathematical Physics;
- High Energy Physics - Theory;
- Mathematics - Quantum Algebra;
- 17B75 (Primary);
- 81R10;
- 17B60;
- 16W50
- E-Print:
- Speakable and unspeakable in gravitational physics: testing gravity from submillimiter to cosmic scale. Proceedings of the VIII Mexican School on Gravitation and Mathematical Physics, Playa del Carmen, Quintana Roo, MEXICO, Dec 2009, 8 pages