# Super-Hopf realizations of Lie Superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map

@inproceedings{KKanakoglou2010SuperHopfRO, title={Super-Hopf realizations of Lie Superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map}, author={K.Kanakoglou and C.Daskaloyannis and A. Herrera-Aguilar Ifm and Univ. of Michoacan and Morelia and Michoac{\'a}n and Mexico Aristotle Univ. of Thessaloniki and Thessaloniki and Greece.}, year={2010} }

The mathematical structure of a mixed paraparticle system ( co bining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be describe d for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it wil l be shown that these realizations possess the valuable representation-theoretic property o f transferring invariably the super-Hopf structure. Finally two…

## 5 Citations

### On a class of Fock-like representations for Lie Superalgebras

- Mathematics
- 2011

Utilizing Lie superalgebra (LS) realizations via the Relative Parabose Set algebra $P_{BF}$, combined with earlier results on the Fock-like representations of $P_{BF}^{(1,1)}$, we proceed to the…

### Ladder Operators, Fock-Spaces, Irreducibility and Group Gradings for the Relative Parabose Set Algebra

- Mathematics
- 2011

The Fock-like representations of the Relative Parabose Set (Rpbs) algebra in a single parabosonic and a single parafermionic degree of freedom are investigated. It is shown that there is an innite…

### YANG-BAXTER OPERATORS FROM (G,)-LIE ALGEBRAS

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- 2010

The (G,�)-Lie algebras are structures which unify the Lie algebras and Lie superalgebras. We use them to produce solutions for the quantum Yang–Baxter equation. The constant and the…

### Towards applications of graded Paraparticle algebras

- MathematicsHNPS Proceedings
- 2019

An outline is sketched, of applications of the ideas and the mathematical methods presented at the 19th symposium of the Hnps in Thessaloniki, May 2010

### Gradings, Braidings, Representations, Paraparticles: Some Open Problems

- MathematicsAxioms
- 2012

A couple of Hamiltonians is proposed, suitable for modeling the radiation matter interaction via a parastatistical algebraic model.

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