L. A-M. HANNA

A note on the matrix representations of the Lie algebras Lr for quantized Hamiltonians where rs=0

Pages: 149-154
Received: 16 February 1998   
Mathematics Subject Classification (2000): 17B81

Abstract: Consider the Lie algebras L^s_r: [K₊,K_-]=sK₀,[K₀,K_±]= ± rK_±; r,s in R, K₀ is a Hermitian operator and K_-= K⁺₊. In [4], [5] the faithful matrix representations of L^s_r and ^c L^s_r were discussed for rsdifferent from 0. In this note we consider the case rs = 0. We prove L⁰₀ has three types of faithful 3-dimensional representations, as the least dimension, while L^s₀,s different from 0 and L⁰_r,r different from 0. In this note we consider the case rs = 0. We prove L⁰₀ has three types of faithful 3-dimensional representations, as the least dimension, while L^s₀,s different from 0 and L⁰_r,r different from 0 have none.