Salih Celik

Differential geometry of the q-superplane

Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which are obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given.

Z3-graded differential geometry of the quantum plane

In this work, the Z3-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. the universal enveloping algebra of the quantum plane is explicitly constructed.

Differential geometry of the Z3-graded quantum superplane

In this work, differential geometry of the Z

On the differential geometry of

_3

Two parameter deformation of Grassmann matrix group and supergroup

-graded quantum superplane is constructed. The corresponding quantum Lie superalgebra and its Hopf algebra structure are obtained.

The Hopf algebra structure of the Z3-graded quantum supergroup GLq,j(1/1)

The differential calculus on the quantum supergroup GL

Cartan calculi on the quantum superplane

_q(1| 1)

COMMENT ON THE DIFFERENTIAL CALCULUS ON THE QUANTUM EXTERIOR PLANE

was introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We construct a differential calculus on the quantum supergroup GL

DIFFERENTIAL GEOMETRY OF THE q-PLANE

_q(1| 1)

Hopf algebra structure of Grq(1|1) related to GLq(1|1)

in a different way and we obtain its quantum superalgebra. The main structures are derived without an R-matrix. It is seen that the found results can be written with help of a matrix