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

  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.},
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… 

On a class of Fock-like representations for Lie Superalgebras

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

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


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

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

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



Lie Algebras and Applications

Basic Concepts.- Semisimple Lie Algebras.- Lie Groups.- Lie Algebras and Lie Groups.- Homogeneous and Symmetric Spaces (Coset Spaces). - Irreducible Bases (Representations).- Casimir Operators and

Hopf algebras and their actions on rings

Definitions and examples Integrals and semisimplicity Freeness over subalgebras Action of finite-dimensional Hopf algebras and smash products Coradicals and filtrations Inner actions Crossed products

Dictionary on lie algebras and superalgebras

Prolegomena. List of Tables. Main Notations. Lie Algebras. Lie Superalgebras. Tables. Bibliography. Index.

Angular Momentum in Quantum Physics: Theory and Application

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The Theory of Lie Superalgebras

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