# Group theoretical foundations of fractional supersymmetry

@article{Azcrraga1995GroupTF, title={Group theoretical foundations of fractional supersymmetry}, author={Jos{\'e} A. de Azc{\'a}rraga and Alan J. Macfarlane}, journal={Journal of Mathematical Physics}, year={1995}, volume={37}, pages={1115-1127} }

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 formula is given in the case of general n for the transformations that leave the theory invariant, and it is shown that these transformations possess interesting group properties. It is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as…

## 60 Citations

### Fractional supersymmetry and Fth-roots of representations

- Mathematics
- 1999

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…

### Local Fractional Supersymmetry for Alternative Statistics

- Mathematics, Physics
- 1995

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…

### Fractional Supersymmetry and F − fold Lie

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- 2003

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…

### Field Theoretic Realizations for Cubic Supersymmetry

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- 2003

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.…

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

- Mathematics
- 1997

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

### NON-ABELIAN FRACTIONAL SUPERSYMMETRY IN TWO DIMENSIONS

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- 2000

Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing Uq(sl(2,ℝ)) at roots of unity. Its representations and the matrix elements are obtained. The dual of it is…

### Fractional supersymmetry and hierarchy of shape invariant potentials

- Physics
- 2006

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…

### Fractional Super-Multi-Virasoro Algebra

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- 2000

An n-dimensional fractional supersymmetry theory is algebraically constructedon the n-dimensional multicomplex space Mn. By emphasizing its appearanceas a special case of generalized Clifford algebra…

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