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 dynamics on the worldvolume from classical cohomology.
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)
Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.
Quantum integrable model of an arrangement of hyperplanes.
Quantum integrable systems
Quantum invariants of links and 3-valent graphs in 3-manifolds
Quantum isometries and group dual subgroups
We study the discrete groups whose duals embed into a given compact quantum group, . In the matrix case the embedding condition is equivalent to having a quotient map , where is a certain family of groups associated to . We develop here a number of techniques for computing , partly inspired from Bichon’s classification of group dual subgroups . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...
Quantum isometry group for spectral triples with real structure.
Quantum link invariant from the Lie superalgebra .
Quantum Racah coefficients and subrepresentation semirings.