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.
Quantum sections and Gauge algebras.
Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates...
Quantum spaces: notes and comments on a lecture by S. L. Woronowicz
Quantum stochastic convolution cocycles -algebraic and C*-algebraic
We summarise recent results concerning quantum stochastic convolution cocycles in two contexts-purely algebraic and C*-algebraic. In each case the class of cocycles arising as the solution of a quantum stochastic differential equation is characterised and the form taken by the stochastic generator of a *-homomorphic cocycle is described. Throughout the paper a common viewpoint on the algebraic and C*-algebraic situations is emphasised; the final section treats the unifying example of convolution...
Quantum-classical interactions and galois type extensions
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle...
Quasi-bigèbres jacobiennes