arXiv subjects
Publications and source records attributed to E. H. Zakkari.
In this paper, we construct a covariant differential calculus on quantum plane with two-parametric quantum group as a symmetry group. The two cases $d^2=0$ and $d^3=0$ are completly established. We also construct differential calculi $n=2$ and $n=3$ nilpotent on super quantum space with one and two-parametric symmetry quantum supergroup.
The splitting of a $Q$-deformed boson, in the $Q\to q=e^{\frac{\QTR{rm}{2πi}}{\QTR{rm}{k}}}$ limit, is discussed. The equivalence between a $Q$-fermion and an ordinary one is established. The properties of the quantum (super)Virasoro algebras 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.
We construct an associative differential algebra on a two-parameter quantum plane associated with a nilpotent endomorphism $d$ in the two cases $d^{2}=0$ and $d^3=0$ $(d^2\neq 0).$ The correspondent curvature is derived and the related non commutative gauge field theory is introduced.
In this paper, we study the fractional decomposition of the quantum enveloping affine algebras $U_Q(\hat A(n))$ and $U_Q(\hat{C}(n))$ with vanishing central charge in the limit $Q\to q=e^{\frac{2iπ}k}$ . This decomposition is based on the bosonic representation and can be related to the fractional supersymmetry and $k$-fermionic spin. The equivalence between the quantum affine algebras and the classical ones in the fermionic realization is also established.
We discuss the algebra of $N\times N$ matrices as a reduced quantum plane. A $3-$nilpotent deformed differential calculus involving a complex parameter $q$ is constructed. The two cases, $q$ $3^{rd}$ and $N^{th}$ root of unity are completely treated. As application, a gauge field theory for the particular cases $n=2$ and $n=3$ is established.