6533b857fe1ef96bd12b4283
RESEARCH PRODUCT
Star-products and phase space realizations of quantum groups
Lu Zhi-chengsubject
AlgebraPure mathematicsSubalgebraCartan matrixCartan subalgebraReal formStatistical and Nonlinear PhysicsKilling formKac–Moody algebraMathematical PhysicsMathematicsLie conformal algebraGraded Lie algebradescription
It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-05-01 | Letters in Mathematical Physics |