scholarly journals Polynomial algebras on coadjoint orbits of semisimple Lie groups

2002 ◽  
Vol 170 (1) ◽  
pp. 29-34
Author(s):  
Mark J. Gotay ◽  
Janusz Grabowski ◽  
Bryon Kaneshige
Keyword(s):  
Lie Groups ◽  
Coadjoint Orbits ◽  
Semisimple Lie Groups ◽  
Polynomial Algebras

scholarly journals DEFORMATION QUANTIZATION OF COADJOINT ORBITS

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2397-2400 ◽  
Author(s):  
M. A. LIEDÓ
Keyword(s):  
Lie Groups ◽  
Algebraic Structure ◽  
Deformation Quantization ◽  
Geometric Quantization ◽  
Coadjoint Orbits ◽  
Semisimple Lie Groups

A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.

scholarly journals Representations of complex semisimple Lie groups and Lie algebras

1966 ◽  
Vol 72 (3) ◽  
pp. 522-526 ◽  
Author(s):  
K. R. Parthasarathy ◽  
R. Ranga Rao ◽  
V. S. Varadarajan
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Semisimple Lie Groups ◽  
Complex Semisimple

The Darboux coordinate system and Holstein–Primakoff representations on Kähler manifolds

2006 ◽  
Vol 84 (10) ◽  
pp. 891-904
Author(s):  
J R Schmidt
Keyword(s):  
Coordinate System ◽  
Lie Groups ◽  
Lie Algebra ◽  
Poisson Structure ◽  
Kähler Manifolds ◽  
Coadjoint Orbits ◽  
Kahler Manifolds ◽  
Canonical Transformations ◽  
Kahler Geometry

The Kahler geometry of minimal coadjoint orbits of classical Lie groups is exploited to construct Darboux coordinates, a symplectic two-form and a Lie–Poisson structure on the dual of the Lie algebra. Canonical transformations cast the generators of the dual into Dyson or Holstein–Primakoff representations.PACS Nos.: 02.20.Sv, 02.30.Ik, 02.40.Tt

Sign in / Sign up

Export Citation Format

Share Document