Search results for "Quantum group"
showing 10 items of 32 documents
Integrability Conditions: Recent Results in the Theory of Integrable Models
1990
This paper reports various results achieved recently in the theory of integrable models. These are summarised in the Fig.1! At the Chester meeting [1] two of the authors were concerned [1] with the local Riemann-Hilbert problem (double-lined box in the centre of Fig.1), its limit as a non-local Riemann-Hilbert problem used to solve classical integrable models in 2+1 dimensions (two space and one time dimensions) [2,3], and the connection of this Riemann-Hilbert problem with Ueno’s [4] Riemann-Hilbert problem associated with the representation of the algebra gl(∞) in terms of Z⊗Z matrices (Z the integers) and the solution of the K-P equations in 2+1. We were also concerned [1] with the const…
A quantum group for the Einstein's equations
2011
In this paper, we expose the construction of a possible, simple matrix quantum group structure (according to Woronowicz), related to elementary formal aspects of the Einstein field equations of General Relativity, and their possible symmetries.
Compact Topological Quantum Groups
1995
Using vector spaces topologies we unify the different models of quantum groups. Duality and reflexivity are built in. The Drinfeld deformation can be extended to the distributions on a simple compact Lie group and dually to the infinitely differentiable functions. The topological quantum double is similarly defined and a uniqueness result is obtained.
The quantum chiral Minkowski and conformal superspaces
2010
We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum supergroups on the quantum Minkowski and quantum conformal superspaces are presented.
Closedness of Star Products and Cohomologies
1994
We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called “closed star products” and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.
Noncompact Topological Quantum Groups
1995
A star-product construction of quantum semisimple real Lie groups is performed for the noncompact case.
On Chiral Quantum Superspaces
2011
We give a quantum deformation of the chiral Minkowski superspace in 4 dimensions embedded as the big cell into the chiral conformal superspace. Both deformations are realized as quantum homogeneous superspaces: we deform the ring of regular functions together with a coaction of the corresponding quantum supergroup.
Remarks on quantum groups
1991
We give a Poisson-bracket realization of SL q (2) in the phase space ℝ2. We then discuss the physical meaning of such a realization in terms of a modified (regularized) toy model, the nonregularized version of which is due to Klauder. Some general remarks and suggestions are also presented in this Letter.
Invariant Markov semigroups on quantum homogeneous spaces
2019
Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant functionals are established. Adding a positivity condition, this yields one-to-one correspondences of invariant quantum Markov semigroups acting on expected coideal *-subalgebras and certain convolution semigroups of states on the underlying compact quantum group. This gives an approach to classifying invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators …
Unitary Representations of U q (𝔰𝔩}(2,ℝ)),¶the Modular Double and the Multiparticle q -Deformed¶Toda Chain
2002
The paper deals with the analytic theory of the quantum q-deformed Toda chains; the technique used combines the methods of representation theory and the Quantum Inverse Scattering Method. The key phenomenon which is under scrutiny is the role of the modular duality concept (first discovered by L. Faddeev) in the representation theory of noncompact semisimple quantum groups. Explicit formulae for the Whittaker vectors are presented in terms of the double sine functions and the wave functions of the N-particle q-deformed open Toda chain are given as a multiple integral of the Mellin–Barnes type. For the periodic chain the two dual Baxter equations are derived.