Geometrical Foundations of Fractional Supersymmetry

Dunne, R. S.; Macfarlane, Alan; Azcárraga, J. A. de; Bueno, J. C. Pérez

doi:10.1142/s0217751x97001729

Cited by 35 publications

(53 citation statements)

References 42 publications

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“…where D q ± are q-derivatives with respect to η ± . This is the same with the realization of supercharges given in [4]- [7], obtained in terms of q-calculus.…”

Section: Quasi-regular Corepresentation Ofsupporting

confidence: 64%

Two-dimensional fractional supersymmetry from the quantum Poincaré group at roots of unity

Ahmedov

Dayi

1999

J. Phys. A: Math. Gen.

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“…where D q ± are q-derivatives with respect to η ± . This is the same with the realization of supercharges given in [4]- [7], obtained in terms of q-calculus.…”

Section: Quasi-regular Corepresentation Ofsupporting

confidence: 64%

Two-dimensional fractional supersymmetry from the quantum Poincaré group at roots of unity

Ahmedov

Dayi

1999

J. Phys. A: Math. Gen.

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“…We will now i n troduce the new set of generators (15) which are the dening relations of a k-fermion [23,24] …”

Section: Fractional Spin Through Q-bosonsmentioning

confidence: 99%

K-Fractional spin through Q-deformed (super)-algebras

Mansour

Daoud

Hassouni

1999

Reports on Mathematical Physics

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The splitting of a Q-deformed boson, in the Q ! q = e 2i k limit, is discussed. The equivalence between a Q-fermion and an ordinary one is established. The properties of quantum algebras U Q (sl(m)), the quantum superalgebras osp Q (1=2m) and U Q (sl(m=1)) and the deformed Virasoro algebra when their deformation parameter Q goes to a root of unity, are investigated. These properties are shown to be related to fractional supersymmetry and k-fermionic spin.

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“…Fractional supersymmetry (FSUSY) [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] is among the possible extensions of supersymmetry which have been studied in the literature. Basically, in such extensions, the generators of the Poincaré algebra are obtained as F −fold (F ∈ N ⋆ ) symmetric products of more fundamental generators.…”

Section: Introductionmentioning

confidence: 99%

Finite-dimensional Lie algebras of order F

Traubenberg

Slupinski

2002

Journal of Mathematical Physics

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F −Lie algebras are natural generalisations of Lie algebras (F = 1) and Lie superalgebras (F = 2). When F > 2 not many finite-dimensional examples are known. In this paper we construct finitedimensional F −Lie algebras F > 2 by an inductive process starting from Lie algebras and Lie superalgebras. Matrix realisations of F −Lie algebras constructed in this way from su(n), sp(2n) so(n) and sl(n|m), osp(2|m) are given. We obtain non-trivial extensions of the Poincaré algebra by Inönü-Wigner contraction of certain F −Lie algebras with F > 2.

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Geometrical Foundations of Fractional Supersymmetry

Abstract: A deformed q-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the *

Cited by 35 publications

References 42 publications

Two-dimensional fractional supersymmetry from the quantum Poincaré group at roots of unity

Two-dimensional fractional supersymmetry from the quantum Poincaré group at roots of unity

K-Fractional spin through Q-deformed (super)-algebras

Finite-dimensional Lie algebras of order F

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