DIFFERENTIAL CALCULUS ON A THREE-PARAMETER OSCILLATOR ALGEBRA

Basics of Algebra, Topology, and Differential Calculus

Two - Parameter Differential Calculus on the h - Exterior Plane

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. This work was supported in part by T. B. T. A. K. the Turkish Scientific and Technical Research Council. E-mail address: [email protected] E-mail address: [email protected]

On extended umbral calculus, oscillator-like algebras and Generalized Clifford Algebra

Some quantum algebras build from deformed oscillator algebras ala Jordan-Schwinger may be described in terms of a particular case of psi-calculus. We give here an example of a specific relation between such certain quantum algebras and generalized Clifford algebras also in the context of Levy-Leblond's azimuthal quantization of angular momentum which was interpreted afterwards as the finite dim...

Schubert Calculus on a Grassmann Algebra

The (classical, small quantum, equivariant) cohomology ring of the grassmannianG(k, n) is generated by certain derivations operating on an exterior algebra of a free module of rank n (Schubert Calculus on a Grassmann Algebra). Our main result gives, in a unified way, a presentation of all such cohomology rings in terms of generators and relations. It also provides, by results of Laksov and Thor...

A General q-Oscillator Algebra

It is well-known that the Macfarlane-Biedenharn q-oscillator and its generalization has no Hopf structure, whereas the Hong Yan q-oscillator can be endowed with a Hopf structure. In this letter, we demonstrate that it is possible to construct a general q-oscillator algebra which includes the Macfarlane-Biedenharn oscillator algebra and the Hong Yan oscillator algebra as special cases. E-mail ad...