Fractional supersymmetry and Fth-roots of representations

@article{Traubenberg1999FractionalSA,
  title={Fractional supersymmetry and Fth-roots of representations},
  author={Michel Rausch de Traubenberg and Marcus J. Slupinski},
  journal={Journal of Mathematical Physics},
  year={1999},
  volume={41},
  pages={4556-4571}
}
A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of three-dimensional fractional supersymmetry in this framework needs some care. The proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation D of any Lie algebra g. This involves taking the Fth-roots of D in an appropriate sense. A fractional… 
View PDF on arXiv
45 Citations
Highly Influential Citations
2
Background Citations
11
Methods Citations
8

Figures from this paper

45 Citations

Fractional Supersymmetry and F − fold Lie

It is generally held that supersymmetry is the only non-trivial extension of the Poincaré algebra. This point of view is based on the two theorems [1, 2]. However, as usual, if some of the…

Fractional supersymmetry and infinite dimensional lie algebras

Field Theoretic Realizations for Cubic Supersymmetry

We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincare algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems.…

Fractional supersymmetry and hierarchy of shape invariant potentials

Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in…

Deformations, Contractions and Classification of Lie Algebras of Order 3

Lie algebras of order F (or F −Lie algebras) are possible generalisations of Lie algebras (F = 1) and Lie superalgebras (F = 2). These structures have been used to implement new non-trivial…

Finite dimensional Lie algebras of order F

F-Lie algebras are natural generalizations of Lie algebras (F=1) and Lie superalgebras (F=2). When F>2 not many finite-dimensional examples are known. In this article we construct finite-dimensional…

About Filiform Lie Algebras of Order 3

The aim of this work is to review recent advances in generalizing filiform Lie (super)algebras into the theory of Lie algebras of order F. Recall that the latter type of algebras constitutes the…

Two approaches to fractional supersymmetrical quantum mechanics

Two complementary approaches of = 2 fractional supersymmetrical quantum mechanics of order k are studied in this article. The first, based on a generalized Weyl–Heisenberg algebra Wk (which comprises…

Some Results on Cubic and Higher Order Extensions of the Poincare Algebra

In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincare algebra. We first give some general properties of Lie superalgebras with some emphasis on…

On Supersymmetric Quantum Mechanics

This paper constitutes a review on N = 2 fractional supersym-metric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W k . It is…

References

SHOWING 1-10 OF 52 REFERENCES

Group theoretical foundations of fractional supersymmetry

Fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized Grassmann variable, θ=θ,θn=0, for arbitrary integer n=2,3,.... An explicit…

Nontrivial Extensions of the 3D-Poincaré Algebra and Fractional Supersymmetry for Anyons

Nontrivial extensions of three-dimensional Poincare algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three-dimensional generalizations of…

2D fractional supersymmetry for rational conformal field theory: Application for third-integer spin states

Z3 ‐graded algebras and the cubic root of the supersymmetry translations

A generalization of supersymmetry is proposed based on Z3 ‐graded algebras. Introducing the objects whose ternary commutation relations contain the cubic roots of unity, e2πi/3, e4πi/3 and 1, the…

Local Fractional Supersymmetry for Alternative Statistics

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to…

All possible generators of supersymmetries of the S-matrix

2D fractional supersymmetry and conformal field theory for alternative statistics

Fractional Superspace Formulation of Generalized Super-Virasoro Algebras

We present a fractional superspace formulation of the centerless parasuper- Virasoro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro…

Fractional Supersymmetries in Perturbed Coset Cfts and Integrable Soliton Theory

Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras

This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes…
...