-analog of Gelfand-Graev basis for the noncompact quantum algebra .
-boson in quantum integrable systems.
-deformation of the Virasoro algebra and lattice conformal theories
-deformed bi-local fields. II.
Quantised -differential algebras
We propose a definition of a quantised -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of are natural examples of such algebras.
Quantization of Poisson Hamiltonian systems
In this paper we recall the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.
Quantization of semisimple real Lie groups
We provide a novel construction of quantized universal enveloping -algebras of real semisimple Lie algebras, based on Letzter’s theory of quantum symmetric pairs. We show that these structures can be ‘integrated’, leading to a quantization of the group C-algebra of an arbitrary semisimple algebraic real Lie group.
Quantizations of braided derivations. I: Monoidal categories.
Quantizations of braided derivations. II: Graded modules.
Quantizations of braided derivations. III: Modules with action by a group.
Quantized semisimple Lie groups
The goal of this expository paper is to give a quick introduction to -deformations of semisimple Lie groups. We discuss principally the rank one examples of , , and related algebras. We treat quantized enveloping algebras, representations of , generalities on Hopf algebras and quantum groups, -structures, quantized algebras of functions on -deformed compact semisimple groups, the Peter-Weyl theorem, -Hopf algebras associated to complex semisimple Lie groups and the Drinfeld double, representations...
Quantum Affine Algebras and Deformations of the Virasoro and -Algebras
Quantum affine algebras, combinatorics of Young walls, and global bases.
Quantum (Co)Modules for Dual Quantum Groups
Quantum curve in -oscillator model.
Quantum deformations and superintegrable motions on spaces with variable curvature.
Quantum deformations of the Lorentz group. The Hopf-algebra level
Quantum Fibre Bundles. An Introduction
An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.
Quantum fields on noncommutative spacetimes: theory and phenomenology.
Quantum groups in higher genus and Drinfeld’s new realizations method ( case)