Fractional Supersymmetry and Lie Algebras

M. Rausch de Traubenberg (1, 2)

1 LPTH - Laboratoire de Physique Théorique
2 PMT - Laboratoire de Physique Mathématique et Théorique

Supersymmetry and super-Lie algebras have been consistently generalized previously. The so-called fractional supersymmetry and $F-$Lie algebras could be constructed starting from any representation $\D$ of any Lie algebra $g$. This involves taking the $F^{\mathrm th}$ root of $\D$ in some sense. We show, after having constructed differential realization(s) of any Lie algebra, how fractional supersymmetry can be explicitly realized in terms of appropriate homogeneous monomials.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Théorie des représentations [math.RT]; Physique des Hautes Energies - Théorie [hep-th]

M. Rausch de Traubenberg. Fractional Supersymmetry and Lie Algebras. Non Commutative Geometry and Superstring Theory, 2000, Rabat, Morocco. ⟨hal-00023290⟩