Local Fractional Supersymmetry for Alternative Statistics

A group theory justification of one dimensional fractional supersymmetry is proposed using an analogue of a coset space, just like the one introduced in $1D$ supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry {\it i.e.} a fractional supergravity which is then quantized {\it \`a la Dirac} to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given, by means of a curved fractional superline.Comment: 15 pages, latex, no figur

Fractional Supersymmetry and Fth-Roots of Representations

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 supersymmetry in any space-time dimension is then possible. This formalism finally leads to an infinite dimensional extension of g, reducing to the centerless Virasoro algebra when g=sl(2,R).Comment: 23 pages, 1 figure, LaTex file with epsf.st

Engagement de groupe, transformation des représentations sociales et modifications comportementales

Dans cette recherche, on s\u27intéresse à la modification d\u27une représentation sociale et à l\u27émission d\u27un comportement. Dans une première condition, les groupes sont composés de personnes « familières », dans la seconde condition, elles ne se connaissent pas. De plus, chaque groupe est divisé en deux sous-groupes, selon qu\u27il y a ou non signature d\u27un document. Il est, ensuite, demandé, aux étudiants, de participer à la mise en place d\u27une campagne de promotion et de valorisation des études. Les résultats montrent des modifications importantes, au niveau des éléments de la représentation sociale, ainsi qu\u27une acceptation plus importante du comportement demandé par l\u27expérimentateur, pour les sujets engagés et familiers. (French

On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge

A model of gravitation with global U(1)-symmetry

It is shown that an embedding of the general relativity $4-$space into a flat $12-$space gives a model of gravitation with the global $U(1)-$symmetry and the discrete $D_{1}-$one. The last one may be transformed into the $SU(2)-$symmetry of the unified model, and the demand of independence of $U(1)-$ and $SU(2)-$transformations leads to the estimate $\sin^{2}\theta_{min}=0,20$ where $\theta_{min}$ is an analog of the Weinberg angle of the standard model.Comment: 7 page