Quantum de Rham complex on 𝔸h1|2

  title={Quantum de Rham complex on 𝔸h1|2},
  author={Salih Celik},
  journal={Journal of Algebra and Its Applications},
  • S. Celik
  • Published 14 November 2018
  • Mathematics, Geology
  • Journal of Algebra and Its Applications
Introducing [Formula: see text]- and [Formula: see text]-deformations of [Formula: see text]-graded ([Formula: see text])- and ([Formula: see text])-spaces, denoted by [Formula: see text] and [Formula: see text], a two-parameter differential calculus, the quantum de Rham complex, on [Formula: see text] are explicitly constructed. It is shown that in contrast to the standard [Formula: see text]-deformation of [Formula: see text], the above complex is unique for [Formula: see text]. The quantum… 
1 Citations


  • S. Celik
  • Reports on Mathematical Physics
  • 2023



Quantization of Lie groups and Lie algebras

The Algebraic Bethe Ansatz, which is the essence of the quantum inverse scattering method, emerges as a natural development of the following different directions in mathematical physics: the inverse

Differential calculus on compact matrix pseudogroups (quantum groups)

The paper deals with non-commutative differential geometry. The general theory of differential calculus on quantum groups is developed. Bicovariant bimodules as objects analogous to tensor bundles

Differential calculus on the quantum superspace and deformation of phase space

AbstractWe investigate non-commutative differential calculus on the supersymmetric version of quantum space in which quantum supergroups are realized. Multiparametric quantum deformation of the

Multiparametric quantum deformation of the general linear supergroup

In the work L. D. Faddeev and his collaborators, and subsequently V. G. Drinfeld, M. Jimbo, S. L. Woronowicz, a new class of Hopf algebras was constructed. They can be considered as one-parametric

On the quantum differential calculus and the quantum holomorphicity

Under some natural assumptions [less restrictive than in the paper by Wess and Zumino (preprint CERN‐TH‐5697/90, LAPP‐TH‐284/90)] differential calculi on the quantum plane are found and investigated.

Notes on quantum groups and quantum de Rham complexes

De Rham complexes of quantum spaces and quantum groups are studied by means of extension of the “universal co-action” technique to the differential algebras.

Bicovariant differential calculus on the quantum superspace ℝq(1|2)

Super-Hopf algebra structure on the function algebra on the extended quantum superspace has been defined. It is given a bicovariant differential calculus on the superspace. The corresponding

On the Contraction of Groups and Their Representations.

  • E. InonuE. Wigner
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1953
The purpose of the present note is to investigate, in some generality, in which sense groups can be limiting cases of other groups, and how their representations can be obtained from the representations of the groups of which they appear as limits.

Covariant differential calculus on the quantum hyperplane

Two-Parametric Extension of h-Deformation of GL(1|1)

The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL(1|1) via a contraction of GLp,q(1|1) is presented. Related differential calculus on the quantum