arXiv subjects
Publications and source records attributed to Salih Celik.
We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We also give a two-parameter deformation of the (1+1)-dimensional phase space algebra.
In this Letter, we introduce the Hopf algebra structure of the quantum quaternionic group GL(1,H$_q)$ and discuss the isomorphism between the quantum symplectic group SP$_q(1)$ and the quantum unitary group SU$_q(2)$.
We construct a right-invariant differential calculus on the quantum supergroup GL$_h(1| 1)$ and obtain the $h$-deformed superalgebra of GL$_h(1| 1)$.
The $h$-deformation of functions on the Grassmann matrix group $Gr(2)$ is presented via a contraction of $Gr_q(2)$. As an interesting point, we have seen that, in the case of the $h$-deformation, both R-matrices of $GL_h(2)$ and $Gr_h(2)$ are the same.
The differential calculus on the quantum supergroup GL$_q(1| 1)$ 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$_q(1| 1)$ 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 $\hat{R}$
We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.
We give a two-parameter quantum deformation of the exterior plane and its differential calculus without the use of any R-matrix and relate it to the differential calculus with the R-matrix. We prove that there are two types of solutions of the Yang-Baxter equation whose symmetry group is $GL_{p,q}(2)$. We also give a two-parameter deformation of the fermionic oscillator algebra.
Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.
In this article it is explicitly shown that the matrix elements of CP$_q(n)$ are the annihilation operator of Pusz-Woronowicz (P-W) oscillators provided they are rescaled.
We introduce the h-deformation of the algebra of functions on the grassmann supergroup Gr$(1|1)$ via a contraction of Gr$_q(1|1)$.
The two parameter quantum deformation of 2x2 Grassmann matrices, Gr(2), and supermatrices, Gr$(1| 1)$, are presented. Gr(2) whose matrix elements are all Grassmannian variables is called the superdual of the genel linear group GL(2), and Gr$(1| 1)$ whose diagonal matrix elements are Grassmannian variables is called the superdual of the supergroup GL$(1| 1)$ whose nondiagonal elements are Grassmannian. Noncentral dual superdeterminant for Grassmann supermatrices belonging to Gr$_{p,q}(1| 1)$ is constructed. As with the 2x2 quantum matrices, the relations satisfied by the matrix elements of the Grassmann matrices are expressed in terms of an $\hat{R}$-matrix. The properties of $n$th power of a Grassmann supermatrix are given as an Appendix.
The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL$(1| 1)$ via a contraction of GL$_{p,q}(1| 1)$ is presented. Related differential calculus on the quantum superplane is introduced.
We introduce a construction of the differential calculus on the quantum supergroup GL$_{p,q}(1| 1)$. We obtain two differential calculi, respectively, associated with the left and right Cartan-Maurer one-forms. We also obtain the quantum superalgebra of GL$_{p,q}(1| 1)$. Although all of the structures we obtain are derived without an R matrix, they neverthless can be expressed using an R matrix.
We show that the algebra of functions on the Grassmann supergroup Gr$_q(1| 1)$ has a (graded) Hopf algebra structure related to GL$_q(1| 1)$.
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
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
In this work, differential geometry of the Z$_3$-graded quantum superplane is constructed. The corresponding quantum Lie superalgebra and its Hopf algebra structure are obtained.