New representations of the Poincaré group describing two interacting bosons
New solutions for Yang-Baxter systems.
Noncommutative 3-sphere as an example of noncommutative contact algebras
The notion of deformation quantization was introduced by F.Bayen, M.Flato et al. in [1]. The basic idea is to formally deform the pointwise commutative multiplication in the space of smooth functions on a symplectic manifold to a noncommutative associative multiplication, whose first order commutator is proportional to the Poisson bracket. It is of interest to compute this quantization for naturally occuring cases. In this paper, we discuss deformations of contact algebras and give a definition...
Noncommutative extensions of the Fourier transform and its logarithm
We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm to the algebra (S) of complex-valued functions on the free semigroup S = FS(z,w) on two generators. First, to given probability measures μ, ν with all moments finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (ℬ,ε,Δ) on two self-adjoint generators X,X’ and a projection P. Then we introduce and study cumulants which are additive under the convolution μ̂* ν̂ = μ̂ ⊗ ν̂ ∘ Δ when...
Noncommutative geometry: fuzzy spaces, the Groenewold-Moyal plane.
Non-commutative Markov processes in free groups factors, related to Berezin's quantization and automorphic forms.
Non-commutative mechanics in mathematical and in condensed matter physics.
Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials.
Notes on TQFT wire models and coherence equations for triangular cells.
Number operator algebras.
On Discrete Frames Associated with Semidirect Products.
On ergodic properties of convolution operators associated with compact quantum groups
Recent results of M. Junge and Q. Xu on the ergodic properties of the averages of kernels in noncommutative -spaces are applied to the analysis of almost uniform convergence of operators induced by convolutions on compact quantum groups.
On Nambu bracket representations of 3-algebras.
On parametrization of the linear and unitary groups in terms of Dirac matrices.
On quantum de Rham cohomology theory.
On quantum weyl algebras and generalized quons
The model of generalized quons is described in an algebraic way as certain quasiparticle states with statistics determined by a commutation factor on an abelian group. Quantization is described in terms of quantum Weyl algebras. The corresponding commutation relations and scalar product are also given.
On solutions of the KZ and qKZ equations at level zero
On solutions to the twisted Yang-Baxter equation
On spin and modularity in conformal field theory
On the contraction of the discrete series of
It is shown, using techniques inspired by the method of orbits, that each non-zero mass, positive energy representation of the Poincaré group can be obtained via contraction from the discrete series of representations of .