The su(n) Lie algebraic structures in the Pegg-Barnett quantization formulation

We investigate the oscillator algebra of the Pegg-Barnett oscillator with a finite-dimensional number-state space and show that it possesses the su($n$) Lie algebraic structure. In addition, a so-called supersymmetric Pegg-Barnett oscillator is suggested, and the related topics such as the algebraic structure and particle occupation number of the Pegg-Barnett oscillator are briefly discussed.