arXiv subjects

Nguyen Viet Hai

Publications and source records attributed to Nguyen Viet Hai.

4 recordsLinked to original sources

arXiv2000

Quantum co-adjoint orbits of $\MD_4$-groups

Using $\star$-product on Co-adjoint orbits (K-orbits) of the $\MD_4$- groups we obtain quantum half-planes, quantum hyperbolic cylinders, quantum hyperbolic paraboloids...via Fedosov deformation quantization. From this we have corresponding unitary representations of the $\MD_4$- groups. Particularly, for groups $\G_{4,2,3(ϕ)}; \G_{4,2,4}; \G_{4,3,4(ϕ)}$ and $ \G_{4,4,1} $, which are neither nilpotent nor exponential, we obtain the explicit formulas.

math.QA↗

arXiv2000

Quantum Co-Adjoint Orbits of the Real Diamond Group

We present explicit formulas for deformation quantization on the co-adjoint orbits of the real diamond Lie group. From this we obtain quantum half-plans, quantum hyperbolic cylinders, quantum hyperbolic paraboloids via Fedosov deformation quantization and finally, the corresponding unitary representations of this group.

math.QA↗

arXiv1999

Quantum Co-Adjoint Orbits of the Group of Affine Transformations of the Complex Straight Line

We construct start-products on the co-adjoint orbit of Lie group $\Aff({\bf C})$ of affine transformations of the complex straight line and apply them to obtain the irreducible unitary representations of this group. These results show effectiveness of the Fedosov quantization even for groups which are neither nilpotent nor exponential. Together with the result for the group $\Aff({\bf R})$ in math.QA/9905002, we have thus a description of quantum $\bar{MD}$ co-adjoint orbits.

math.QA↗

arXiv1999

Quantum Half-Planes via Deformation Quantization

We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an exact computation of the star-product and the operator $\hat{\ell}_Z$, we show that the resulting representations exhausted all the irreducible representations of this groups.

math.QA↗