On the problem of classifying simple compact quantum groups
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.
On the set-theoretical Yang-Baxter equation.
On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.
One-dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.
Para-Grassmann variables and coherent states.
Poisson Lie groups and their relations to quantum groups
The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic facts about...
Power of a determinant with two physical applications.
-analog of Gelfand-Graev basis for the noncompact quantum algebra .
-boson in quantum integrable systems.
-deformed bi-local fields. II.
-deformed superspace and -extended supersymmetric Hamiltonian with arbitrary superpotential
-Wakimoto modules and integral formulae of solutions of the quantum Knizhnik-Zamolodchikov equations.
q-deformed circularity for an unbounded operator in Hilbert space
The notion of strong circularity for an unbounded operator is introduced and studied. Moreover, q-deformed circularity as a q-analogue of circularity is characterized in terms of the partially isometric and the positive parts of the polar decomposition.
Quantum Affine Algebras and Deformations of the Virasoro and -Algebras
Quantum algebras and associated with certain -Hahn polynomials: a revisited approach.
Quantum curve in -oscillator model.
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 homogeneous superspaces and quantum duality principle
We define the concept of quantum section of a line bundle of a homogeneous superspace and we employ it to define the concept of quantum homogeneous projective superspace. We also suggest a generalization of the QDP to the quantum supersetting.
Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.