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

Quantum Co-adjoint Orbits of the Group of Affine Transformations of the Complex Straight Line Do Ngoc Diep and Nguyen Viet Hai

We construct start-products on the co-adjoint orbit of the Lie group Aff(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(R) [see DH], we have ...

Quantum Co-adjoint Orbits of the Real Diamond Group

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

Adjoint and Coadjoint Orbits of the Poincaré Group

In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we c...

Characterizing Global Minimizers of the Difference of Two Positive Valued Affine Increasing and Co-radiant Functions

‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

On One-Sided Ideals of Rings of Linear Transformations